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Chapter 5 Resource Masters - Math Classmrsstuckeysmathclass.weebly.com/.../alg1_ch5_answers.pdfy of...
22
Chapter 5 Resource Masters
Transcript of Chapter 5 Resource Masters - Math Classmrsstuckeysmathclass.weebly.com/.../alg1_ch5_answers.pdfy of...
Chapter 5Resource Masters
© Glencoe/McGraw-Hill A2 Glencoe Algebra 1
Stu
dy
Gu
ide
and I
nte
rven
tion
Slo
pe
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-1
5-1
©G
lenc
oe/M
cGra
w-H
ill28
1G
lenc
oe A
lgeb
ra 1
Lesson 5-1
Find
Slo
pe
Slo
pe o
f a
Line
m!
or m
!, w
here
(x 1
, y1)
and
(x 2
, y2)
are
the
coor
dina
tes
of a
ny tw
o po
ints
on
a no
nver
tical
line
y 2"
y 1# x 2
"x 1
rise
# run
Fin
d t
he
slop
e of
th
eli
ne
that
pas
ses
thro
ugh
(!
3,5)
and
(4,
!2)
.
Let
("
3,5)
!(x
1,y 1
) an
d (4
,"2)
!(x
2,y 2
).
m!
Slo
pe fo
rmul
a
!y 2
!"
2, y
1!
5, x
2!
4, x
1!
"3
!S
impl
ify.
!"
1
"7
#7"
2 "
5#
#4
"("
3)
y 2"
y 1# x 2
"x 1
Fin
d t
he
valu
e of
rso
th
at
the
lin
e th
rou
gh (
10,r
) an
d (
3,4)
has
a
slop
e of
!.
m!
Slo
pe fo
rmul
a
"!
m!
", y
2!
4, y
1!
r, x
2!
3, x
1!
10
"!
Sim
plify
.
"2(
"7)
!7(
4 "
r)C
ross
mul
tiply
.
14 !
28 "
7rD
istr
ibut
ive
Pro
pert
y
"14
!"
7rS
ubtr
act 2
8 fr
om e
ach
side
.
2 !
rD
ivid
e ea
ch s
ide
by "
7.
4 "
r#
"7
2 # 7
2 # 74
"r
# 3 "
102 # 7
y 2"
y 1# x 2
"x 1
2 " 7
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d t
he
slop
e of
th
e li
ne
that
pas
ses
thro
ugh
eac
h p
air
of p
oin
ts.
1.(4
,9),
(1,6
)1
2.("
4,"
1),(
"2,
"5)
!2
3.("
4,"
1),(
"4,
"5)
unde
fined
4.(2
,1),
(8,9
)5.
(14,
"8)
,(7,
"6)
!6.
(4,"
3),(
8,"
3)0
7.(1
,"2)
,(6,
2)8.
(2,5
),(6
,2)
!9.
(4,3
.5),
("4,
3.5)
0
Det
erm
ine
the
valu
e of
rso
th
e li
ne
that
pas
ses
thro
ugh
eac
h p
air
of p
oin
ts h
asth
e gi
ven
slo
pe.
10.(
6,8)
,(r,
"2)
,m!
1!
411
.("
1,"
3),(
7,r)
,m!
312
.(2,
8),(
r,"
4) m
!"
36
13.(
7,"
5),(
6,r)
,m!
0!
514
.(r,
4),(
7,1)
,m!
1115
.(7,
5),(
r,9)
,m!
6
16.(
10,r
),(3
,4),
m!
"17
.(10
,4),
("2,
r),m
!"
0.5
18.(
r,3)
,(7,
r),m
!"
210
2
1 # 52 # 7
23 " 33 # 4
3 # 4
3 " 44 " 5
2 " 74 " 3
©G
lenc
oe/M
cGra
w-H
ill28
2G
lenc
oe A
lgeb
ra 1
Rate
of
Chan
geT
he r
ate
of c
han
gete
lls,o
n av
erag
e,ho
w a
qua
ntit
y is
cha
ngin
g ov
erti
me.
Slop
e de
scri
bes
a ra
te o
f ch
ange
.
POPU
LATI
ON
Th
e gr
aph
sh
ows
the
pop
ula
tion
gro
wth
in
Ch
ina.
a.F
ind
th
e ra
tes
of c
han
ge f
or 1
950–
1975
an
d f
or
1975
–200
0.
1950
–197
5:! !
or 0
.015
2
1975
–200
0:! !
or 0
.012
4
b.E
xpla
in t
he
mea
nin
g of
th
e sl
ope
in e
ach
cas
e.F
rom
195
0–19
75,t
he g
row
th w
as 0
.015
2 bi
llion
per
yea
r,or
15.
2 m
illio
n pe
r ye
ar.
Fro
m 1
975–
2000
,the
gro
wth
was
0.0
124
billi
on p
er y
ear,
or 1
2.4
mill
ion
per
year
.
c.H
ow a
re t
he
dif
fere
nt
rate
s of
ch
ange
sh
own
on
th
e gr
aph
?T
here
is a
gre
ater
ver
tica
l cha
nge
for
1950
–197
5 th
an f
or 1
975–
2000
.The
refo
re,t
hese
ctio
n of
the
gra
ph f
or 1
950–
1975
has
a s
teep
er s
lope
.
LON
GEV
ITY
Th
e gr
aph
sh
ows
the
pre
dic
ted
lif
e ex
pec
tan
cy f
or m
en a
nd
wom
en b
orn
in
a g
iven
yea
r.
1.F
ind
the
rate
s of
cha
nge
for
wom
en fr
om 2
000–
2025
an
d 20
25–2
050.
0.16
/yr,
0.12
/yr
2.F
ind
the
rate
s of
cha
nge
for
men
from
200
0–20
25 a
nd20
25–2
050.
0.16
/yr,
0.12
/yr
3.E
xpla
in t
he m
eani
ng o
f yo
ur r
esul
ts in
Exe
rcis
es 1
an
d 2.
Bot
h m
en a
nd w
omen
incr
ease
d th
eir
life
expe
ctan
cy a
t th
e sa
me
rate
s.4.
Wha
t pa
tter
n do
you
see
in t
he in
crea
se w
ith
each
25
-yea
r pe
riod
?W
hile
life
exp
ecta
ncy
incr
ease
s,it
does
not
incr
ease
at
a co
nsta
nt r
ate.
5.M
ake
a pr
edic
tion
for
the
life
exp
ecta
ncy
for
2050
–207
5.E
xpla
in h
ow y
ou a
rriv
ed a
tyo
ur p
redi
ctio
n.S
ampl
e an
swer
:89
for
wom
en a
nd 8
3 fo
r m
en;t
hede
crea
se in
rat
e fr
om 2
000–
2025
to
2025
–205
0 is
0.0
4/yr
.If
the
decr
ease
in t
he r
ate
rem
ains
the
sam
e,th
e ch
ange
of
rate
for
2050
–207
5 m
ight
be
0.08
/yr
and
25(0
.08)
#2
year
s of
incr
ease
ove
r th
e 25
-yea
r sp
an.
Pred
icti
ng
Lif
e Ex
pec
tan
cy
Year
Bor
n
Age
2000
Wom
enM
en
100 95 90 85 80 75 70 65
2050
*20
25*
*Est
imat
ed
Sour
ce: U
SA T
ODA
Y8084
8178
74
87
0.31
#251.24
"0.
93#
#20
00 "
1975
chan
ge in
pop
ulat
ion
##
#ch
ange
in t
ime
0.38
#250.
93 "
0.55
##
1975
"19
50ch
ange
in p
opul
atio
n#
##
chan
ge in
tim
e
Pop
ula
tio
n G
row
th i
n C
hin
a
Year
People (billions)
1950
1975
2000
2.0
1.5
1.0
0.5 0
2025
*
*Est
imat
ed
Sour
ce: U
nite
d Na
tions
Pop
ulat
ion
Divis
ion
0.55
0.93
1.24
1.48
Stu
dy
Gu
ide
and I
nte
rven
tion
(c
onti
nued
)
Slo
pe
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-1
5-1
Exer
cises
Exer
cises
Exam
ple
Exam
ple
Answers (Lesson 5-1)
© Glencoe/McGraw-Hill A3 Glencoe Algebra 1
Ans
wer
s
Skil
ls P
ract
ice
Slo
pe
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-1
5-1
©G
lenc
oe/M
cGra
w-H
ill28
3G
lenc
oe A
lgeb
ra 1
Lesson 5-1
Fin
d t
he
slop
e of
th
e li
ne
that
pas
ses
thro
ugh
eac
h p
air
of p
oin
ts.
1.2.
3.
2!
3
4.(2
,5),
(3,6
)1
5.(6
,1),
("6,
1)0
6.(4
,6),
(4,8
)un
defin
ed7.
(5,2
),(5
,"2)
unde
fined
8.(2
,5),
("3,
"5)
29.
(9,8
),(7
,"8)
8
10.(
"5,
"8)
,("
8,1)
!3
11.(
"3,
10),
("3,
7)un
defin
ed
12.(
17,1
8),(
18,1
7)!
113
.("
6,"
4),(
4,1)
14.(
10,0
),("
2,4)
!15
.(2,
"1)
,("
8,"
2)
16.(
5,"
9),(
3,"
2)!
17.(
12,6
),(3
,"5)
18.(
"4,
5),(
"8,
"5)
19.(
"5,
6),(
7,"
8)!
Fin
d t
he
valu
e of
rso
th
e li
ne
that
pas
ses
thro
ugh
eac
h p
air
of p
oin
ts h
as t
he
give
n s
lop
e.
20.(
r,3)
,(5,
9),m
!2
221
.(5,
9),(
r,"
3),m
!"
48
22.(
r,2)
,(6,
3),m
!4
23.(
r,4)
,(7,
1),m
!11
24.(
5,3)
,(r,
"5)
,m!
43
25.(
7,r)
,(4,
6),m
!0
6
3 # 41 # 2
7 " 65 " 2
11 " 97 " 2
1 " 101 " 3
1 " 2
1 " 3
( 0, 1
) ( 1, –
2)x
y
O
( 0, 0
)( 3, 1
)
x
y
O( 0
, 1)( 2
, 5)
x
y O
©G
lenc
oe/M
cGra
w-H
ill28
4G
lenc
oe A
lgeb
ra 1
Fin
d t
he
slop
e of
th
e li
ne
that
pas
ses
thro
ugh
eac
h p
air
of p
oin
ts.
1.2.
3.
!3
0
4.(6
,3),
(7,"
4)!
75.
("9,
"3)
,("
7,"
5)!
1
6.(6
,"2)
,(5,
"4)
27.
(7,"
4),(
4,8)
!4
8.("
7,8)
,("
7,5)
unde
fined
9.(5
,9),
(3,9
)0
10.(
15,2
),("
6,5)
!11
.(3,
9),(
"2,
8)
12.(
"2,
"5)
,(7,
8)13
.(12
,10)
,(12
,5)
unde
fined
14.(
0.2,
"0.
9),(
0.5,
"0.
9)0
15. !
,", !
",
"F
ind
th
e va
lue
of r
so t
he
lin
e th
at p
asse
s th
rou
gh e
ach
pai
r of
poi
nts
has
th
egi
ven
slo
pe.
16.(
"2,
r),(
6,7)
,m!
317
.("
4,3)
,(r,
5),m
!4
18.(
"3,
"4)
,("
5,r)
,m!
"5
19.(
"5,
r),(
1,3)
,m!
!4
20.(
1,4)
,(r,
5),m
unde
fine
d1
21.(
"7,
2),(
"8,
r),m
!"
57
22.(
r,7)
,(11
,8),
m!
"16
23.(
r,2)
,(5,
r),m
!0
2
24.R
OO
FIN
GT
he p
itch
of a
roo
f is
the
num
ber
of f
eet
the
roof
ris
es f
or e
ach
12 f
eet
hori
zont
ally
.If
a ro
of h
as a
pit
ch o
f 8,
wha
t is
its
slop
e ex
pres
sed
as a
pos
itiv
e nu
mbe
r?
25. S
ALE
SA
dai
ly n
ewsp
aper
had
12,
125
subs
crib
ers
whe
n it
beg
an p
ublic
atio
n.F
ive
year
sla
ter
it h
ad 1
0,10
0 su
bscr
iber
s.W
hat
is t
he a
vera
ge y
earl
y ra
te o
f ch
ange
in t
he n
umbe
rof
sub
scri
bers
for
the
fiv
e-ye
ar p
erio
d?!
405
subs
crib
ers
per
year
2 " 3
1 # 5
7 # 69 # 2
1 # 41 # 2
1 " 42 # 3
1 # 34 # 3
7 # 3
13 " 9
1 " 51 " 7
4 " 5
( –2,
3)
( 3, 3
)
x
y O
( 3, 1
)
( –2,
–3)
x
y
O( –
1, 0
)
( –2,
3)
x
y
OPra
ctic
e (A
vera
ge)
Slo
pe
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-1
5-1
Answers (Lesson 5-1)
© Glencoe/McGraw-Hill A4 Glencoe Algebra 1
Rea
din
g t
o L
earn
Math
emati
csS
lope
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-1
5-1
©G
lenc
oe/M
cGra
w-H
ill28
5G
lenc
oe A
lgeb
ra 1
Lesson 5-1
Pre-
Act
ivit
yW
hy
is s
lop
e im
por
tan
t in
arc
hit
ectu
re?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 5-
1 at
the
top
of
page
256
in y
our
text
book
.The
n co
mpl
ete
the
defi
niti
on o
f sl
ope
and
fill
in t
he b
oxes
on t
he g
raph
wit
h th
e w
ords
ris
ean
d ru
n.
slop
e !
In t
his
grap
h,th
e ri
se is
un
its,
and
the
run
is
unit
s.
Thu
s,th
e sl
ope
of t
his
line
is
or
.
Read
ing
the
Less
on1.
Des
crib
e ea
ch t
ype
of s
lope
and
incl
ude
a sk
etch
.Ty
pe o
f S
lope
Des
crip
tion
of G
raph
Ske
tch
posi
tive
The
grap
h ri
ses
as y
ou g
o fr
om le
ft t
o ri
ght.
nega
tive
The
grap
h fa
lls a
s yo
u go
fro
m le
ft t
o ri
ght.
zero
The
grap
h is
a h
oriz
onta
l lin
e.
unde
fined
The
grap
h is
a v
ertic
al li
ne.
2.D
escr
ibe
how
eac
h ex
pres
sion
is r
elat
ed t
o sl
ope.
a.di
ffer
ence
of
y-co
ordi
nate
s di
vide
d by
diff
eren
ce o
fco
rres
pond
ing
x-co
ordi
nate
sb.
how
far
up
or d
own
as c
ompa
red
to h
ow f
ar le
ft o
r ri
ght
c.sl
ope
used
as
rate
of
chan
ge
Hel
ping
You
Rem
embe
r3.
The
wor
d ri
seis
usu
ally
ass
ocia
ted
wit
h go
ing
up.S
omet
imes
goi
ng f
rom
one
poi
nt o
nth
e gr
aph
does
not
invo
lve
a ri
se a
nd a
run
but
a f
all a
nd a
run
.Des
crib
e ho
w y
ou c
ould
sele
ct p
oint
s so
tha
t it
is a
lway
s a
rise
fro
m t
he f
irst
poi
nt t
o th
e se
cond
poi
nt.
Sam
ple
answ
er:I
f th
e sl
ope
is n
egat
ive,
choo
se t
he s
econ
d po
int
so t
hat
its x
-coo
rdin
ate
is le
ss t
han
that
of
the
first
poi
nt.
$52,
000
incr
ease
in s
pend
ing
""
""
26 m
onth
s
rise
" run
y 2#
y 1" x 2
#x 1
x
y
O
x
y
O
x
y
O
x
y
O
3 " 53
unit
s" 5
unit
s
53
rise
" run
x
y
O
rise
run
©G
lenc
oe/M
cGra
w-H
ill28
6G
lenc
oe A
lgeb
ra 1
Trea
sure
Hun
t w
ith S
lope
sU
sin
g th
e d
efin
itio
n o
f sl
ope,
dra
w l
ines
wit
h t
he
slop
es l
iste
d
belo
w.A
cor
rect
sol
uti
on w
ill
trac
e th
e ro
ute
to
the
trea
sure
.
1.3
2.3.
#4.
0
5.1
6.#
17.
no s
lope
8.
9.10
.11
.#
12.
33 " 4
1 " 33 " 2
2 " 7
2 " 51 " 4
Star
t Her
e
Trea
sure
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-1
5-1
Answers (Lesson 5-1)
© Glencoe/McGraw-Hill A5 Glencoe Algebra 1
Ans
wer
s
Stu
dy
Gu
ide
and I
nte
rven
tion
Slo
pe a
nd D
irec
t Var
iatio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-2
5-2
©G
lenc
oe/M
cGra
w-H
ill28
7G
lenc
oe A
lgeb
ra 1
Lesson 5-2
Dir
ect
Vari
atio
nA
dir
ect
vari
atio
nis
des
crib
ed b
y an
equ
atio
n of
the
for
m y
!kx
,w
here
k$
0.W
e sa
y th
at y
var
ies
dire
ctly
as
x.In
the
equ
atio
n y
!kx
,kis
the
con
stan
t of
var
iati
on.
Nam
e th
e co
nst
ant
ofva
riat
ion
for
th
e eq
uat
ion
.Th
en f
ind
the
slop
e of
th
e li
ne
that
pas
ses
thro
ugh
th
e p
air
of p
oin
ts.
For
y!
x,th
e co
nsta
nt o
f var
iati
on is
.
m!
Slo
pe fo
rmul
a
!(x
1, y
1) !
(0, 0
), (
x 2, y
2) !
(2, 1
)
!S
impl
ify.
The
slo
pe is
.
1 # 2
1 # 21 "
0# 2
"0
y 2"
y 1# x 2
"x 1
1 # 21 # 2
( 2, 1
)( 0
, 0)
x
y
Oy
! 1 2x
Su
pp
ose
yva
ries
dir
ectl
y as
x,a
nd
y#
30 w
hen
x#
5.
a.W
rite
a d
irec
t va
riat
ion
equ
atio
nth
at r
elat
es x
and
y.
Fin
d th
e va
lue
of k
.y
!kx
Dire
ct v
aria
tion
equa
tion
30 !
k(5)
Rep
lace
yw
ith 3
0 an
d x
with
5.
6 !
kD
ivid
e ea
ch s
ide
by 5
.
The
refo
re,t
he e
quat
ion
is y
!6x
.
b.U
se t
he
dir
ect
vari
atio
n e
quat
ion
to
fin
d x
wh
en y
#18
.y
!6x
Dire
ct v
aria
tion
equa
tion
18 !
6xR
epla
ce y
with
18.
3 !
xD
ivid
e ea
ch s
ide
by 6
.
The
refo
re,x
!3
whe
n y
!18
.
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Nam
e th
e co
nst
ant
of v
aria
tion
for
eac
h e
quat
ion
.Th
en d
eter
min
e th
e sl
ope
of t
he
lin
e th
at p
asse
s th
rou
gh e
ach
pai
r of
poi
nts
.
1.2.
3.
!2;
!2
3;3
;
Wri
te a
dir
ect
vari
atio
n e
quat
ion
th
at r
elat
es x
to y
.Ass
um
e th
at y
vari
es d
irec
tly
as x
.Th
en s
olve
.
4.If
y!
4 w
hen
x!
2,fi
nd y
whe
n x
!16
.y
#2x
;32
5.If
y!
9 w
hen
x!
"3,
find
xw
hen
y!
6.y
#!
3x;!
26.
If y
!"
4.8
whe
n x
!"
1.6,
find
x w
hen
y!
"24
.y
#3x
;!8
7.If
y!
whe
n x
!,f
ind
xw
hen
y!
.y
#2x
;3 " 32
3 # 161 # 8
1 # 4
3 " 23 " 2( –
2, –
3)
( 0, 0
)x
y O
y !
3 2x
( 1, 3
)
( 0, 0
)x
y
O
y !
3x
( –1,
2)
( 0, 0
)x
y
Oy
! –
2x
©G
lenc
oe/M
cGra
w-H
ill28
8G
lenc
oe A
lgeb
ra 1
Solv
e Pr
oble
ms
The
dis
tan
ce f
orm
ula
d!
rtis
a d
irec
t va
riat
ion
equa
tion
.In
the
form
ula,
dist
ance
dva
ries
dir
ectl
y as
tim
e t,
and
the
rate
ris
the
con
stan
t of
var
iati
on.
TRA
VEL
A f
amil
y d
rove
th
eir
car
225
mil
es i
n 5
hou
rs.
a.W
rite
a d
irec
t va
riat
ion
equ
atio
n t
o fi
nd
th
e d
ista
nce
tra
vele
d f
or a
ny
nu
mbe
rof
hou
rs.
Use
giv
en v
alue
s fo
r d
and
tto
fin
d r.
d!
rtO
rigin
al e
quat
ion
225
!r(
5)d
!22
5 an
d t!
5
45!
rD
ivid
e ea
ch s
ide
by 5
.
The
refo
re,t
he d
irec
t va
riat
ion
equa
tion
is d
!45
t.b.
Gra
ph
th
e eq
uat
ion
.T
he g
raph
of d
!45
tpa
sses
thr
ough
the
ori
gin
wit
hsl
ope
45.
m!
✓C
HEC
K(5
,225
) lie
s on
the
gra
ph.
c.E
stim
ate
how
man
y h
ours
it
wou
ld t
ake
the
fam
ily
to d
rive
360
mil
es.
d!
45t
Orig
inal
equ
atio
n
360
!45
tR
epla
ce d
with
360
.
t!
8D
ivid
e ea
ch s
ide
by 4
5.
The
refo
re,i
t w
ill t
ake
8 ho
urs
to d
rive
360
mile
s.
RET
AIL
Th
e to
tal
cost
Cof
bu
lk j
elly
bea
ns
is
$4.4
9 ti
mes
th
e n
um
ber
of p
oun
ds
p.
1.W
rite
a d
irec
t va
riat
ion
equa
tion
tha
t re
late
s th
e va
riab
les.
C#
4.49
p2.
Gra
ph t
he e
quat
ion
on t
he g
rid
at t
he r
ight
.
3.F
ind
the
cost
of
poun
d of
jelly
bea
ns.
$3.3
7
CH
EMIS
TRY
Ch
arle
s’s
Law
sta
tes
that
,at
a co
nst
ant
pre
ssu
re,v
olu
me
of a
gas
Vva
ries
dir
ectl
y as
its
tem
per
atu
reT
.A v
olu
me
of 4
cu
bic
feet
of
a ce
rtai
n g
as h
as a
tem
per
atu
reof
200
°(a
bsol
ute
tem
per
atu
re).
V#
0.02
T4.
Wri
te a
dir
ect
vari
atio
n eq
uati
on t
hat
rela
tes
the
vari
able
s.
5.G
raph
the
equ
atio
n on
the
gri
d at
the
rig
ht.
5 ft
3
6.F
ind
the
volu
me
of t
he s
ame
gas
at 2
50°
(abs
olut
e te
mpe
ratu
re).
Ch
arle
s’s
Law
Tem
pera
ture
($K
)
Volume (cubic feet)
100
020
0T
V 4 3 2 1
3 # 4
Co
st o
f Je
lly
Bea
ns
Wei
ght
(pou
nds)
Cost (dollars)
20
4w
C
18.0
0
13.5
0
9.00
4.50
rise
# run
45 # 1
Au
tom
ob
ile
Trip
s
Tim
e (h
ours
)
Distance (miles)
10
23
45
67
8t
d
360
270
180 90
( 1, 4
5)
( 5, 2
25)
d !
45t
Stu
dy
Gu
ide
and I
nte
rven
tion
(c
onti
nued
)
Slo
pe a
nd D
irec
t Var
iatio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-2
5-2
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 5-2)
© Glencoe/McGraw-Hill A6 Glencoe Algebra 1
Skil
ls P
ract
ice
Slo
pe a
nd D
irec
t Var
iatio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-2
5-2
©G
lenc
oe/M
cGra
w-H
ill28
9G
lenc
oe A
lgeb
ra 1
Lesson 5-2
Nam
e th
e co
nst
ant
of v
aria
tion
for
eac
h e
quat
ion
.Th
en d
eter
min
e th
e sl
ope
of t
he
lin
e th
at p
asse
s th
rou
gh e
ach
pai
r of
poi
nts
.
1.;
2.!
2;!
23.
!;
!
Gra
ph
eac
h e
quat
ion
.
4.y
!3x
5.y
!"
x6.
y!
x
Wri
te a
dir
ect
vari
atio
n e
quat
ion
th
at r
elat
es x
and
y.A
ssu
me
that
yva
ries
dir
ectl
y as
x.T
hen
sol
ve.
7.If
y!
"8
whe
n x
!"
2,fi
nd x
8.If
y!
45 w
hen
x!
15,f
ind
xw
hen
y!
32.
y#
4x;8
whe
n y
!15
.y
#3x
;5
9.If
y!
"4
whe
n x
!2,
find
y10
.If
y!
"9
whe
n x
!3,
find
yw
hen
x!
"6.
y#
!2x
;12
whe
n x
!"
5.y
#!
3x;1
5
11.I
f y
!4
whe
n x
!16
,fin
d y
12.I
f y
!12
whe
n x
!18
,fin
d x
whe
n x
!6.
y#
x;w
hen
y!
"16
.y
#x;
!24
Wri
te a
dir
ect
vari
atio
n e
quat
ion
th
at r
elat
es t
he
vari
able
s.T
hen
gra
ph
th
eeq
uat
ion
.
13. T
RA
VEL
The
tot
al c
ost
Cof
gas
olin
e
14.S
HIP
PIN
GT
he n
umbe
r of
del
iver
ed t
oys
Tis
$1.
80 t
imes
the
num
ber
of g
allo
ns g
.is
3 t
imes
the
tot
al n
umbe
r of
cra
tes
c.C
#1.
80g
T#
3cTo
ys S
hip
ped
Crat
es
Toys
20
46
71
35
c
T 21 18 15 12 9 6 3
Gas
oli
ne
Co
st
Gal
lons
Cost ($)
40
812
142
610
g
C 28 24 20 16 12 8 4
2 " 33 " 2
1 " 4
x
y
O
2 # 5
x
y
O
3 # 4
x
y
O
3 " 23 " 2( –
2, 3
)
( 0, 0
)x
y
O
y !
– 3 2x
( –1,
2)
( 0, 0
)x
y
O
y !
–2x
1 " 31 " 3
( 3, 1
)( 0
, 0)
x
y O
y !
1 3x
©G
lenc
oe/M
cGra
w-H
ill29
0G
lenc
oe A
lgeb
ra 1
Nam
e th
e co
nst
ant
of v
aria
tion
for
eac
h e
quat
ion
.Th
en d
eter
min
e th
e sl
ope
of t
he
lin
e th
at p
asse
s th
rou
gh e
ach
pai
r of
poi
nts
.
1.;
2.;
3.!
;!
Gra
ph
eac
h e
quat
ion
.
4.y
!"
2x5.
y!
x6.
y!
"x
Wri
te a
dir
ect
vari
atio
n e
quat
ion
th
at r
elat
es x
and
y.A
ssu
me
that
yva
ries
dir
ectl
y as
x.T
hen
sol
ve.
7.If
y!
7.5
whe
n x
!0.
5,fi
nd y
whe
n x
!"
0.3.
y#
15x;
!4.
5
8.If
y!
80 w
hen
x!
32,f
ind
xw
hen
y!
100.
y#
2.5x
;40
9.If
y!
whe
n x
!24
,fin
d y
whe
n x
!12
.y
#x;
Wri
te a
dir
ect
vari
atio
n e
quat
ion
th
at r
elat
es t
he
vari
able
s.T
hen
gra
ph
th
eeq
uat
ion
.
10. M
EASU
RE
The
wid
th W
of a
11
.TIC
KET
ST
he t
otal
cos
t C
of t
icke
ts is
rect
angl
e is
tw
o th
irds
of
the
leng
th !
.$4
.50
tim
es t
he n
umbe
r of
tic
kets
t.
W#
!C
#4.
50t
12.P
ROD
UCE
The
cos
t of
ban
anas
var
ies
dire
ctly
wit
h th
eir
wei
ght.
Mig
uel b
ough
t
3po
unds
of
bana
nas
for
$1.1
2.W
rite
an
equa
tion
tha
t re
late
s th
e co
st o
f th
e ba
nana
s
to t
heir
wei
ght.
The
n fi
nd t
he c
ost
of 4
poun
ds o
f ba
nana
s.C
#0.
32p
;$1.
361 # 4
1 # 2
Co
st o
f Ti
cket
s
Tick
ets
Cost ($)
20
46
13
5t
C 25 20 15 10 5
Rec
tan
gle
Dim
ensi
on
s
Leng
th
Width
40
812
26
10!
W 10 8 6 4 2
2 " 3
3 " 81 " 32
3 # 4
x
y
O
5 # 3
x
y
O
6 # 5
x
y
O
5 " 25 " 2
( –2,
5)
( 0, 0
)x
y
O
y !
" 5 2x
4 " 34 " 3
( 3, 4
)
( 0, 0
)x
y O
y !
4 3x
3 " 43 " 4
( 4, 3
)
( 0, 0
)x
y O
y !
3 4x
Pra
ctic
e (A
vera
ge)
Slo
pe a
nd D
irec
t Var
iatio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-2
5-2
Answers (Lesson 5-2)
© Glencoe/McGraw-Hill A7 Glencoe Algebra 1
Ans
wer
s
Rea
din
g t
o L
earn
Math
emati
csS
lope
and
Dir
ect V
aria
tion
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-2
5-2
©G
lenc
oe/M
cGra
w-H
ill29
1G
lenc
oe A
lgeb
ra 1
Lesson 5-2
Pre-
Act
ivit
yH
ow i
s sl
ope
rela
ted
to
you
r sh
ower
?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 5-
2 at
the
top
of
page
264
in y
our
text
book
.
•H
ow d
o th
e nu
mbe
rs in
the
tab
le r
elat
e to
the
gra
ph s
how
n?Th
ey a
re t
he c
oord
inat
es o
f th
e po
ints
on
the
grap
h.
•T
hink
abo
ut t
he f
irst
sen
tenc
e.W
hat
does
it m
ean
to s
ay t
hat
a st
anda
rdsh
ower
head
use
s ab
out
6 ga
llons
of
wat
er p
er m
inut
e?S
ampl
e an
swer
:For
eac
h m
inut
e th
e sh
ower
run
s,6
gallo
nsof
wat
er c
ome
out.
So,
if th
e sh
ower
ran
10
min
utes
,tha
tw
ould
be
60 g
allo
ns.
Read
ing
the
Less
on
1.W
hat
is t
he f
orm
of
a di
rect
var
iati
on e
quat
ion?
y!
kx
2.H
ow is
the
con
stan
t of
var
iati
on r
elat
ed t
o sl
ope?
The
cons
tant
of
vari
atio
n ha
sth
e sa
me
valu
e as
the
slo
pe o
f th
e gr
aph
of t
he e
quat
ion.
3.T
he e
xpre
ssio
n “y
vari
es d
irec
tly
as x
”ca
n be
wri
tten
as
the
equa
tion
y!
kx.H
ow w
ould
you
wri
te a
n eq
uati
on f
or “
wva
ries
dir
ectl
y as
the
squ
are
of t
”?w
!kt
2
4.Fo
r ea
ch s
itua
tion
,wri
te a
n eq
uati
on w
ith
the
prop
er c
onst
ant
of v
aria
tion
.
a.T
he d
ista
nce
dva
ries
dir
ectl
y as
tim
e t,
and
a ch
eeta
h ca
n tr
avel
88
feet
in 1
sec
ond.
d!
88t
b.T
he p
erim
eter
pof
a p
enta
gon
wit
h al
l sid
es o
f eq
ual l
engt
h va
ries
dir
ectl
y as
the
leng
th s
of a
sid
e of
the
pen
tago
n.A
pen
tago
n ha
s 5
side
s.p
!5s
c.T
he w
ages
Wea
rned
by
an e
mpl
oyee
var
y di
rect
ly w
ith
the
num
ber
of h
ours
hth
atar
e w
orke
d.E
nriq
ue e
arne
d $1
72.5
0 fo
r 23
hou
rs o
f w
ork.
W!
$7.5
0h
Hel
ping
You
Rem
embe
r
5.L
ook
up t
he w
ord
cons
tant
in a
dic
tion
ary.
How
doe
s th
is d
efin
itio
n re
late
to
the
term
cons
tant
of
vari
atio
n?S
ampl
e an
swer
:Som
ethi
ng u
ncha
ngin
g;th
e co
nsta
ntof
var
iatio
n re
late
s x
and
yin
the
sam
e va
lue
ever
y tim
e,an
d th
atre
latio
nshi
p ne
ver
chan
ges.
©G
lenc
oe/M
cGra
w-H
ill29
2G
lenc
oe A
lgeb
ra 1
nth
Pow
er V
aria
tion
An
equa
tion
of t
he fo
rm y
!kx
n ,w
here
k"
0,de
scri
bes
an n
th p
ower
vari
atio
n.T
he v
aria
ble
nca
n be
rep
lace
d by
2 t
o in
dica
te t
he s
econ
d po
wer
of x
(the
squ
are
of x
) or
by 3
to
indi
cate
the
thi
rd p
ower
of x
(the
cub
e of
x).
Ass
ume
that
the
wei
ght
of a
per
son
of a
vera
ge b
uild
var
ies
dire
ctly
as
the
cube
of
that
per
son’
s he
ight
.The
equ
atio
n of
var
iati
on h
as t
he f
orm
w
!kh
3 .
The
wei
ght
that
a p
erso
n’s
legs
will
sup
port
is p
ropo
rtio
nal t
o th
e cr
oss-
sect
iona
l are
a of
the
leg
bone
s.T
his
area
var
ies
dire
ctly
as
the
squa
reof
the
per
son’
s he
ight
.The
equ
atio
n of
var
iati
on h
as t
he fo
rm s
!kh
2 .
An
swer
eac
h q
ues
tion
.
1.Fo
r a
pers
on 6
fee
t ta
ll w
ho w
eigh
s 20
0 po
unds
,fin
d a
valu
e fo
r k
in t
he
equa
tion
w!
kh3 .
k!
0.93
2.U
se y
our
answ
er f
rom
Exe
rcis
e 1
to p
redi
ct t
he w
eigh
t of
a p
erso
n w
ho
is 5
fee
t ta
ll.ab
out
116
poun
ds
3.F
ind
the
valu
e fo
r k
in t
he e
quat
ion
w!
kh3
for
a ba
by w
ho is
20
inch
es
long
and
wei
ghs
6 po
unds
.
k!
1.29
6 fo
r h
!ft
4.H
ow d
oes
your
ans
wer
to
Exe
rcis
e 3
dem
onst
rate
tha
t a
baby
is
sign
ific
antl
y fa
tter
in p
ropo
rtio
n to
its
heig
ht t
han
an a
dult
?
kha
s a
grea
ter
valu
e.
5.Fo
r a
pers
on 6
fee
t ta
ll w
ho w
eigh
s 20
0 po
unds
,fin
d a
valu
e fo
r k
in t
he
equa
tion
s!
kh2 .
k!
5.56
6.Fo
r a
baby
who
is 2
0 in
ches
long
and
wei
ghs
6 po
unds
,fin
d an
“in
fant
va
lue”
for
kin
the
equ
atio
n s
!kh
2 .
k!
2.16
for
h!
ft
7.A
ccor
ding
to
the
adul
t eq
uati
on y
ou f
ound
(E
xerc
ise
1),h
ow m
uch
wou
ld a
n im
agin
ary
gian
t 20
fee
t ta
ll w
eigh
?
7440
pou
nds
8.A
ccor
ding
to
the
adul
t eq
uati
on f
or w
eigh
t su
ppor
ted
(Exe
rcis
e 5)
,how
m
uch
wei
ght
coul
d a
20-f
oot
tall
gian
t’s le
gs a
ctua
lly s
uppo
rt?
only
222
4 po
unds
9.W
hat
can
you
conc
lude
fro
m E
xerc
ises
7 a
nd 8
?
Ans
wer
s w
ill v
ary.
For
exam
ple,
bone
str
engt
h lim
its t
he s
ize
hum
ans
can
atta
in.
5 " 35 " 3
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-2
5-2
Answers (Lesson 5-2)
© Glencoe/McGraw-Hill A8 Glencoe Algebra 1
Stu
dy
Gu
ide
an
d I
nte
rven
tion
Slo
pe-In
terc
ept
Form
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-3
5-3
©G
lenc
oe/M
cGra
w-H
ill29
3G
lenc
oe A
lgeb
ra 1
Lesson 5-3
Slop
e-In
terc
ept
Form
Slo
pe-In
terc
ept
Form
y!
mx
#b,
whe
re m
is th
e gi
ven
slop
e an
d b
is th
e y-
inte
rcep
t
Wri
te a
n e
quat
ion
of
the
lin
e w
hos
e sl
ope
is #
4 an
d w
hos
e y-
inte
rcep
t is
3.
y!
mx
#b
Slo
pe-in
terc
ept f
orm
y!
$4x
#3
Rep
lace
mw
ith $
4 an
d b
with
3.
Gra
ph
3x
#4y
!8.
3x$
4y!
8O
rigin
al e
quat
ion
$4y
!$
3x#
8S
ubtr
act 3
xfr
om e
ach
side
.
!D
ivid
e ea
ch s
ide
by $
4.
y!
x$
2S
impl
ify.
The
y-i
nter
cept
of y
!x
$2
is $
2 an
d th
e sl
ope
is
.So
grap
h th
e po
int
(0,$
2).F
rom
this
poi
nt,m
ove
up 3
uni
ts a
nd r
ight
4 u
nits
.Dra
w a
line
pas
sing
thr
ough
bot
h po
ints
.
Wri
te a
n e
quat
ion
of
the
lin
e w
ith
th
e gi
ven
slo
pe
and
y-i
nte
rcep
t.
1.sl
ope:
8,y-
inte
rcep
t $
32.
slop
e:$
2,y-
inte
rcep
t $
13.
slop
e:$
1,y-
inte
rcep
t $
7y
!8x
#3
y!
#2x
#1
y!
#x
#7
Wri
te a
n e
quat
ion
of
the
lin
e sh
own
in
eac
h g
rap
h.
4.5.
6.
y!
2x#
2y
!#
x$
3y
!x
#5
Gra
ph
eac
h e
quat
ion
.
7.y
!2x
#1
8.y
!$
3x#
29.
y!
$x
$1
x
y
Ox
y
Ox
y
O
3 " 4
( 4, –
2)
( 0, –
5)
xy
O
( 3, 0
)
( 0, 3
)
x
y
O( 0
, –2)
( 1, 0
)x
y
O
3 % 43 % 4
3 % 4$3x
#8
%%
$4
$4y
% $4
( 0, –
2)
( 4, 1
)
x
y
O
3x $
4y
! 8
Exam
ple
1Ex
ampl
e 1
Exam
ple
2Ex
ampl
e 2
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill29
4G
lenc
oe A
lgeb
ra 1
Mod
el R
eal-W
orld
Dat
a
MED
IAS
ince
199
7,th
e n
um
ber
of c
able
TV
sys
tem
s h
as d
ecre
ased
by a
n a
vera
ge r
ate
of 1
21 s
yste
ms
per
yea
r.T
her
e w
ere
10,9
43 s
yste
ms
in 1
997.
a.W
rite
a l
inea
r eq
uat
ion
to
fin
d t
he
aver
age
nu
mbe
r of
cab
le s
yste
ms
in a
ny
year
afte
r 19
97.
The
rat
e of
cha
nge
is $
121
syst
ems
per
year
.In
the
firs
t ye
ar,t
he n
umbe
r of
sys
tem
s w
as10
,943
.Let
N!
the
num
ber
of c
able
TV
sys
tem
s.L
et x
!th
e nu
mbe
r of
yea
rs a
fter
199
7.A
n eq
uati
on is
N!
$12
1x#
10,9
43.
b.G
rap
h t
he
equ
atio
n.
The
gra
ph o
f N!
$12
1x#
10,9
43 is
a li
ne t
hat
pass
esth
roug
h th
e po
int
at (
0,10
,943
) an
d ha
s a
slop
e of
$12
1.
c.F
ind
th
e ap
pro
xim
ate
nu
mbe
r of
cab
le T
V
syst
ems
in 2
000.
N!
$12
1x#
10,9
43O
rigin
al e
quat
ion
N!
$12
1(3)
#10
,943
Rep
lace
xw
ith 3
.
N!
10,5
80S
impl
ify.
The
re w
ere
abou
t 10
,580
cab
le T
V s
yste
ms
in 2
000.
ENTE
RTA
INM
ENT
In 1
995,
65.7
% o
f al
l h
ouse
hol
ds
wit
h T
V’s
in
th
e U
.S.s
ubs
crib
ed t
o ca
ble
TV.
Bet
wee
n 1
995
and
199
9,th
e p
erce
nt
incr
ease
d b
y ab
out
0.6%
eac
h y
ear.
1.W
rite
an
equa
tion
to
find
the
per
cent
Pof
hou
seho
lds
that
subs
crib
ed t
o ca
ble
TV
for
any
yea
r x
betw
een
1995
and
199
9.P
!0.
6x$
65.7
2.G
raph
the
equ
atio
n on
the
gri
d at
the
rig
ht.
3.F
ind
the
perc
ent
that
sub
scri
bed
to c
able
TV
in 1
999.
68.1
%
POPU
LATI
ON
Th
e p
opu
lati
on o
f th
e U
nit
ed S
tate
s is
p
roje
cted
to
be 3
00 m
illi
on b
y th
e ye
ar 2
010.
Bet
wee
n
2010
an
d 2
050,
the
pop
ula
tion
is
exp
ecte
d t
o in
crea
se b
yab
out
2.5
mil
lion
per
yea
r.
4.W
rite
an
equa
tion
to
find
the
pop
ulat
ion
Pin
any
yea
r x
betw
een
2010
and
205
0.P
!2,
500,
000x
$30
0,00
0,00
0
5.G
raph
the
equ
atio
n on
the
gri
d at
the
rig
ht.
6.F
ind
the
popu
lati
on in
205
0.ab
out
400,
000,
000
Pro
ject
ed U
nit
edSt
ates
Po
pu
lati
on
Year
s Si
nce
2010
Population (millions)
020
40x
P
400
380
360
340
320
300
Sour
ce: T
he W
orld
Alm
anac
Perc
ent
of
Ho
use
ho
lds
wit
h T
V H
avin
g C
able
Year
s Si
nce
1995
Percent
10
23
45
x
P
68 67 66 65
Sour
ce: T
he W
orld
Alm
anac
Cab
le T
V S
yste
ms
Year
s Si
nce
1997
Number of Cable TV Systems
10
23
45
6x
N
10,9
00
10,8
00
10,7
00
10,6
00
10,5
00
Sour
ce: T
he W
orld
Alm
anac
Stu
dy
Gu
ide
and I
nte
rven
tion
(c
onti
nued
)
Slo
pe-In
terc
ept
Form
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-3
5-3
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 5-3)
© Glencoe/McGraw-Hill A9 Glencoe Algebra 1
Ans
wer
s
Skil
ls P
ract
ice
Slo
pe-In
terc
ept F
orm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-3
5-3
©G
lenc
oe/M
cGra
w-H
ill29
5G
lenc
oe A
lgeb
ra 1
Lesson 5-3
Wri
te a
n e
quat
ion
of
the
lin
e w
ith
th
e gi
ven
slo
pe
and
y-i
nte
rcep
t.
1.sl
ope:
5,y-
inte
rcep
t:"
3y
#5x
!3
2.sl
ope:
"2,
y-in
terc
ept:
7y
#!
2x%
7
3.sl
ope:
"6,
y-in
terc
ept:
"2
y#
!6x
!2
4.sl
ope:
7,y-
inte
rcep
t:1
y#
7x%
1
5.sl
ope:
3,y-
inte
rcep
t:2
y#
3x%
26.
slop
e:"
4,y-
inte
rcep
t:"
9y
#!
4x!
9
7.sl
ope:
1,y-
inte
rcep
t:"
12y
#x
!12
8.sl
ope:
0,y-
inte
rcep
t:8
y#
8
Wri
te a
n e
quat
ion
of
the
lin
e sh
own
in
eac
h g
rap
h.
9.10
.11
.
y#
2x!
3y
#!
3x%
2y
#!
x!
1
Gra
ph
eac
h e
quat
ion
.
12.y
!x
%4
13.y
!"
2x"
114
.x%
y!
"3
Wri
te a
lin
ear
equ
atio
n i
n s
lop
e-in
terc
ept
form
to
mod
el e
ach
sit
uat
ion
.
15.A
vid
eo s
tore
cha
rges
$10
for
a r
enta
l car
d pl
us $
2 pe
r re
ntal
.C
#2r
%10
16.A
Nor
folk
pin
e is
18
inch
es t
all a
nd g
row
s at
a r
ate
of 1
.5 f
eet
per
year
.H
#1.
5t%
1.5
17.A
Cai
rn t
erri
er w
eigh
s 30
pou
nds
and
is o
n a
spec
ial d
iet
to lo
se 2
pou
nds
per
mon
th.
W#
!2m
%30
18.A
n ai
rpla
ne a
t an
alt
itud
e of
300
0 fe
et d
esce
nds
at a
rat
e of
500
fee
t pe
r m
ile.
A#
!50
0m%
3000
x
y
O
x
y
Ox
y
O
( 0, –
1)( 2
, –3)
x
y O
( 0, 2
)
( 2, –
4)
x
y
O( 2
, 1)
( 0, –
3)
x
y
O
©G
lenc
oe/M
cGra
w-H
ill29
6G
lenc
oe A
lgeb
ra 1
Wri
te a
n e
quat
ion
of
the
lin
e w
ith
th
e gi
ven
slo
pe
and
y-i
nte
rcep
t.
1.sl
ope:
,y-i
nter
cept
:3y
#x
%3
2.sl
ope:
,y-i
nter
cept
:"4
y#
x!
4
3.sl
ope:
1.5,
y-in
terc
ept:
"1
4.sl
ope:
"2.
5,y-
inte
rcep
t:3.
5y
#1.
5x!
1y
#!
2.5x
%3.
5
Wri
te a
n e
quat
ion
of
the
lin
e sh
own
in
eac
h g
rap
h.
5.6.
7.
y#
x%
2y
#x
%3
y#
!x
!2
Gra
ph
eac
h e
quat
ion
.
8.y
!"
x%
29.
3y!
2x"
610
.6x
%3y
!6
Wri
te a
lin
ear
equ
atio
n i
n s
lop
e-in
terc
ept
form
to
mod
el e
ach
sit
uat
ion
.
11.A
com
pute
r te
chni
cian
cha
rges
$75
for
a co
nsul
tati
on p
lus
$35
per
hour
.C
#35
h%
75
12.T
he p
opul
atio
n of
Pin
e B
luff
is 6
791
and
is d
ecre
asin
g at
the
rat
e of
7 p
er y
ear.
P#
!7t
%67
91
WR
ITIN
GF
or E
xerc
ises
13–
15,u
se t
he
foll
owin
g in
form
atio
n.
Car
la h
as a
lrea
dy w
ritt
en 1
0 pa
ges
of a
nov
el.S
he p
lans
to w
rite
15
addi
tion
al p
ages
per
mon
th u
ntil
she
is f
inis
hed.
13.W
rite
an
equa
tion
to
find
the
tot
al n
umbe
r of
pag
es P
wri
tten
aft
er a
ny n
umbe
r of
mon
ths
m.
P#
10 %
15m
14.G
raph
the
equ
atio
n on
the
gri
d at
the
rig
ht.
15.F
ind
the
tota
l num
ber
of p
ages
wri
tten
aft
er 5
mon
ths.
85
Car
la’s
No
vel
Mon
ths
Pages Written
20
46
13
5m
P
100 80 60 40 20
x
y
Ox
y
Ox
y
O1 # 2
2 " 33 " 2
2 " 5
( –3,
0)
( 0, –
2)
x
y
O( –
2, 0
)
( 0, 3
)
x
y O( –
5, 0
)
( 0, 2
)
x
y
O
3 " 23 # 2
1 " 41 # 4P
ract
ice
(Ave
rage
)
Slo
pe-In
terc
ept F
orm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-3
5-3
Answers (Lesson 5-3)
© Glencoe/McGraw-Hill A10 Glencoe Algebra 1
Rea
din
g t
o L
earn
Math
emati
csS
lope
-Inte
rcep
t Fo
rm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-3
5-3
©G
lenc
oe/M
cGra
w-H
ill29
7G
lenc
oe A
lgeb
ra 1
Lesson 5-3
Pre-
Act
ivit
yH
ow i
s a
y-in
terc
ept
rela
ted
to
a fl
at f
ee?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 5-
3 at
the
top
of
page
272
in y
our
text
book
.
•W
hat
poin
t on
the
gra
ph s
how
s th
at t
he f
lat
fee
is $
5.00
?(0
,5)
•H
ow d
oes
the
rate
of
$0.1
0 pe
r m
inut
e re
late
to
the
grap
h?It
is t
he s
lope
.
Read
ing
the
Less
on
1.F
ill in
the
box
es w
ith
the
corr
ect
wor
ds t
o de
scri
be w
hat
man
d b
repr
esen
t.
y!
mx
"b
⎯↑↑ ⎯
2.W
hat
are
the
slop
e an
d y-
inte
rcep
t of
a v
erti
cal l
ine?
The
slop
e is
und
efin
ed,a
nd t
here
is n
o y-
inte
rcep
t.
3.W
hat
are
the
slop
e an
d y-
inte
rcep
t of
a h
oriz
onta
l lin
e?
The
slop
e is
0,a
nd t
he y
-inte
rcep
t is
whe
re it
cro
sses
the
y-a
xis.
4.R
ead
the
prob
lem
.The
n an
swer
eac
h pa
rt o
f th
e ex
erci
se.
A r
uby-
thro
ated
hum
min
gbir
d w
eigh
s ab
out
0.6
gram
at
birt
h an
d ga
ins
wei
ght
at a
rat
eof
abo
ut 0
.2 g
ram
per
day
unt
il fu
lly g
row
n.
a.W
rite
a v
erba
l equ
atio
n to
sho
w h
ow t
he w
ords
are
rel
ated
to
find
ing
the
aver
age
wei
ght
of a
rub
y-th
roat
ed h
umm
ingb
ird
at a
ny g
iven
wee
k.U
se t
he w
ords
wei
ght
atbi
rth,
rate
of
grow
th,w
eigh
t,an
d w
eeks
aft
er b
irth
.Bel
ow t
he e
quat
ion,
fill
in a
nyva
lues
you
kno
w a
nd p
ut a
que
stio
n m
ark
unde
r th
e it
ems
that
you
do
not
know
.
!#
"
b.D
efin
e w
hat
vari
able
s to
use
for
the
unk
now
n qu
anti
ties
.S
ampl
e an
swer
:Let
W
be t
he w
eigh
t at
any
tim
e an
d t
be t
he n
umbe
r of
wee
ks a
fter
bir
th.
c.U
se t
he v
aria
bles
you
def
ined
and
wha
t yo
u kn
ow f
rom
the
pro
blem
to
wri
te a
neq
uati
on.
W!
0.2t
"0.
6
Hel
ping
You
Rem
embe
r
5.O
ne w
ay t
o re
mem
ber
som
ethi
ng is
to
expl
ain
it t
o an
othe
r pe
rson
.Wri
te h
ow y
ou w
ould
expl
ain
to s
omeo
ne t
he p
roce
ss f
or u
sing
the
y-i
nter
cept
and
slo
pe t
o gr
aph
a lin
ear
equa
tion
.O
n th
e y-
axis
,plo
t th
e po
int
for
the
y-in
terc
ept.
Then
use
the
rise
-ove
r-ru
n de
finiti
on o
f sl
ope
to d
eter
min
e ho
w f
ar u
p or
dow
n an
dri
ght
or le
ft t
he n
ext
poin
t is
fro
m t
he f
irst
.
y-in
terc
ept
slop
e
wei
ght
?ra
te o
f gr
owth
0.2
wee
ks a
fter
bir
th?
wei
ght
at b
irth
0.6
©G
lenc
oe/M
cGra
w-H
ill29
8G
lenc
oe A
lgeb
ra 1
Rel
atin
g S
lope
-Inte
rcep
t Fo
rm a
nd S
tand
ard
Form
sYo
u ha
ve le
arne
d th
at s
lope
can
be
defi
ned
in t
erm
s of
or
.
Ano
ther
def
init
ion
can
be f
ound
fro
m t
he s
tand
ard
from
of
a lin
ear
equa
tion
.Sta
ndar
d fo
rm is
Ax
"B
y!
C,w
here
A,B
,and
Car
e in
tege
rs,A
$0,
and
Aan
d B
are
not
both
zer
o.
1.So
lve
Ax
"B
y!
C fo
r y.
Your
ans
wer
sho
uld
be w
ritt
en in
sl
ope-
inte
rcep
t fo
rm.
y!
#x
"
2.U
se t
he s
lope
-int
erce
pt e
quat
ion
you
wro
te in
Exe
rcis
e 1
to w
rite
ex
pres
sion
s fo
r th
e sl
ope
and
the
y-in
terc
ept
in t
erm
s of
A,B
,and
C.
m!
#,b
!
Use
th
e ex
pre
ssio
ns
in E
xerc
ise
2 ab
ove
to f
ind
th
e sl
ope
and
y-
inte
rcep
t of
eac
h e
quat
ion
.
3.2x
"y
!%
44.
4x"
3y!
24
m!
#2,
b!
#4
m!
#,b
!8
5.4x
"6y
!%
366.
x%
3y!
%27
m!
#,b
!#
6m
!,b
!9
7.x
%2y
!6
8.4y
!20
m!
,b!
#3
m!
0,b
!5
1 $ 2
1 $ 32 $ 3
4 $ 3
C $ BA $ B
C $ BA $ B
y 2%
y 1& x 2
%x 1
rise
& run
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-3
5-3
Answers (Lesson 5-3)
© Glencoe/McGraw-Hill A11 Glencoe Algebra 1
Ans
wer
s
Stu
dy
Gu
ide
and I
nte
rven
tion
Wri
ting
Equ
atio
ns in
Slo
pe-In
terc
ept F
orm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-4
5-4
©G
lenc
oe/M
cGra
w-H
ill29
9G
lenc
oe A
lgeb
ra 1
Lesson 5-4
Wri
te a
n Eq
uati
on G
iven
the
Slo
pe a
nd O
ne P
oint
Wri
te a
n e
quat
ion
of
a li
ne
that
pas
ses
thro
ugh
(!
4,2)
wit
h s
lop
e 3.
The
line
has
slo
pe 3
.To
find
the
y-
inte
rcep
t,re
plac
e m
wit
h 3
and
(x,y
)w
ith
("4,
2) in
the
slo
pe-i
nter
cept
for
m.
The
n so
lve
for
b.y
!m
x%
bS
lope
-inte
rcep
t for
m
2 !
3("
4) %
bm
!3,
y!
2, a
nd x
!"
4
2 !
"12
%b
Mul
tiply
.
14 !
bA
dd 1
2 to
eac
h si
de.
The
refo
re,t
he e
quat
ion
is y
!3x
%14
.
Wri
te a
n e
quat
ion
of
the
lin
eth
at p
asse
s th
rou
gh (
!2,
!1)
wit
h s
lop
e .
The
line
has
slo
pe
.Rep
lace
mw
ith
and
(x,y
)
wit
h ("
2,"
1) in
the
slo
pe-i
nter
cept
for
m.
y!
mx
%b
Slo
pe-in
terc
ept f
orm
"1
!("
2) %
bm
!, y
!"
1, a
nd x
!"
2
"1
!"
%b
Mul
tiply
.
"!
bA
dd
to e
ach
side
.
The
refo
re,t
he e
quat
ion
is y
!x
".
1 # 21 # 4
1 # 21 # 2
1 # 2
1 # 41 # 4
1 # 41 # 4
1 " 4
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Wri
te a
n e
quat
ion
of
the
lin
e th
at p
asse
s th
rou
gh e
ach
poi
nt
wit
h t
he
give
n s
lop
e.
1.2.
3.
y#
2x!
1y
#!
2xy
#x
%3
4.(8
,2),
m!
"5.
("1,
"3)
,m!
56.
(4,"
5),m
!"
y#
!x
%8
y#
5x%
2y
#!
x!
3
7.("
5,4)
,m!
08.
(2,2
),m
!9.
(1,"
4),m
!"
6
y#
4y
#x
%1
y#
!6x
%2
10.W
rite
an
equa
tion
of
a lin
e th
at p
asse
s th
roug
h th
e y-
inte
rcep
t "
3 w
ith
slop
e 2.
y#
2x!
311
.Wri
te a
n eq
uati
on o
f a
line
that
pas
ses
thro
ugh
the
x-in
terc
ept
4 w
ith
slop
e "
3.y
#!
3x%
1212
.Wri
te a
n eq
uati
on o
f a
line
that
pas
ses
thro
ugh
the
poin
t (0
,350
) w
ith
slop
e .
y#
x%
350
1 " 5
1 # 5
1 " 2
1 # 2
1 " 23 " 4
1 # 23 # 4
1 " 2
( 2, 4
)
x
y
O
m !
1 2
( 0, 0
)x
y
O
m !
–2
( 3, 5
)
x
y
O
m !
2
©G
lenc
oe/M
cGra
w-H
ill30
0G
lenc
oe A
lgeb
ra 1
Wri
te a
n Eq
uati
on G
iven
Tw
o Po
ints
Wri
te a
n e
quat
ion
of
the
lin
e th
at p
asse
s th
rou
gh (
1,2)
an
d (
3,!
2).
Fin
d th
e sl
ope
m.T
o fi
nd t
he y
-int
erce
pt,r
epla
ce m
wit
h it
s co
mpu
ted
valu
e an
d (x
,y)
wit
h(1
,2)
in t
he s
lope
-int
erce
pt f
orm
.The
n so
lve
for
b.
m!
Slo
pe fo
rmul
a
m!
y 2!
"2,
y1
!2,
x2
!3,
x1
!1
m!
"2
Sim
plify
.
y!
mx
%b
Slo
pe-in
terc
ept f
orm
2 !
"2(
1) %
bR
epla
ce m
with
"2,
yw
ith 2
, and
xw
ith 1
.
2 !
"2
%b
Mul
tiply
.
4 !
bA
dd 2
to e
ach
side
.
The
refo
re,t
he e
quat
ion
is y
!"
2x%
4.
Wri
te a
n e
quat
ion
of
the
lin
e th
at p
asse
s th
rou
gh e
ach
pai
r of
poi
nts
.
1.2.
3.
y#
4x!
3y
#!
x%
4y
#x
%1
4.("
1,6)
,(7,
"10
)5.
(0,2
),(1
,7)
6.(6
,"25
),("
1,3)
y#
!2x
%4
y#
5x%
2y
#!
4x!
1
7.("
2,"
1),(
2,11
)8.
(10,
"1)
,(4,
2)9.
("14
,"2)
,(7,
7)
y#
3x%
5y
#!
x%
4y
#x
%4
10.W
rite
an
equa
tion
of
a lin
e th
at p
asse
s th
roug
h th
e x-
inte
rcep
t 4
and
y-in
terc
ept
"2.
y#
x!
2
11.W
rite
an
equa
tion
of
a lin
e th
at p
asse
s th
roug
h th
e x-
inte
rcep
t "
3 an
d y-
inte
rcep
t 5.
y#
x%
5
12.W
rite
an
equa
tion
of
a lin
e th
at p
asse
s th
roug
h (0
,16)
and
("10
,0).
y#
x%
168 " 55 " 31 " 2
3 " 71 " 2
1 " 3( 0, 1
)
( –3,
0)
x
y
O
( 0, 4
) ( 4, 0
)x
y
O
( 1, 1
)
( 0, –
3)
x
y
O
"2
"2
#3
"1
y 2"
y 1# x 2
"x 1St
udy
Gu
ide
and I
nte
rven
tion
(c
onti
nued
)
Wri
ting
Equ
atio
ns in
Slo
pe-In
terc
ept F
orm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-4
5-4
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 5-4)
© Glencoe/McGraw-Hill A12 Glencoe Algebra 1
Skil
ls P
ract
ice
Wri
ting
Equ
atio
ns in
Slo
pe-In
terc
ept F
orm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-4
5-4
©G
lenc
oe/M
cGra
w-H
ill30
1G
lenc
oe A
lgeb
ra 1
Lesson 5-4
Wri
te a
n e
quat
ion
of
the
lin
e th
at p
asse
s th
rou
gh e
ach
poi
nt
wit
h t
he
give
n s
lop
e.
1.2.
3.
y#
!3x
%1
y#
x!
3y
#2x
%4
4.(1
,9),
m!
45.
(4,2
),m
!"
26.
(2,"
2),m
!3
y#
4x%
5y
#!
2x%
10y
#3x
!8
7.(3
,0),
m!
58.
("3,
"2)
,m!
29.
("5,
4),m
!"
4y
#5x
!15
y#
2x%
4y
#!
4x!
16
Wri
te a
n e
quat
ion
of
the
lin
e th
at p
asse
s th
rou
gh e
ach
pai
r of
poi
nts
.
10.
11.
12.
y#
!x
%1
y#
2x!
1y
#!
2x%
3
13.(
1,3)
,("
3,"
5)14
.(1,
4),(
6,"
1)15
.(1,
"1)
,(3,
5)y
#2x
%1
y#
!x
%5
y#
3x!
4
16.(
"2,
4),(
0,6)
17.(
3,3)
,(1,
"3)
18.(
"1,
6),(
3,"
2)y
#x
%6
y#
3x!
6y
#!
2x%
4
Wri
te a
n e
quat
ion
of
the
lin
e th
at h
as e
ach
pai
r of
in
terc
epts
.
19.x
-int
erce
pt:"
3,y-
inte
rcep
t:6
20.x
-int
erce
pt:3
,y-i
nter
cept
:3y
#2x
%6
y#
!x
%3
21.x
-int
erce
pt:1
,y-i
nter
cept
:222
.x-i
nter
cept
:2,y
-int
erce
pt:"
4y
#!
2x%
2y
#2x
!4
23.x
-int
erce
pt:"
4,y-
inte
rcep
t:"
824
.x-i
nter
cept
:"1,
y-in
terc
ept:
4y
#!
2x!
8y
#4x
%4
( 2, –
1)
( 0, 3
)
x
y
O( –
1, –
3)
( 1, 1
)x
y
O
( –2,
3)
( 3, –
2)
x
y
O
( –1,
2)
x
y O
m !
2
( 4, 1
)
x
y
O
m !
1
( –1,
4)
x
y
O
m !
–3
©G
lenc
oe/M
cGra
w-H
ill30
2G
lenc
oe A
lgeb
ra 1
Wri
te a
n e
quat
ion
of
the
lin
e th
at p
asse
s th
rou
gh e
ach
poi
nt
wit
h t
he
give
n s
lop
e.
1.2.
3.
y#
3x!
1y
#!
2x!
2y
#!
x!
4
4.("
5,4)
,m!
"3
5.(4
,3),
m!
6.(1
,"5)
,m!
"
y#
!3x
!11
y#
x%
1y
#!
x!
Wri
te a
n e
quat
ion
of
the
lin
e th
at p
asse
s th
rou
gh e
ach
pai
r of
poi
nts
.
7.8.
9.
y#
x!
6y
#!
x%
5y
#!
2x!
5
10.(
0,"
4),(
5,"
4)11
.("
4,"
2),(
4,0)
12.(
"2,
"3)
,(4,
5)
y#
!4
y#
x!
1y
#x
!
13.(
0,1)
,(5,
3)14
.("
3,0)
,(1,
"6)
15.(
1,0)
,(5,
"1)
y#
x%
1y
#!
x!
y#
!x
%
Wri
te a
n e
quat
ion
of
the
lin
e th
at h
as e
ach
pai
r of
in
terc
epts
.
16.x
-int
erce
pt:2
,y-i
nter
cept
:"5
17.x
-int
erce
pt:2
,y-i
nter
cept
:10
y#
x!
5y
#!
5x%
10
18.x
-int
erce
pt:"
2,y-
inte
rcep
t:1
19.x
-int
erce
pt:"
4,y-
inte
rcep
t:"
3
y#
x%
1y
#!
x!
3
20.D
AN
CE
LESS
ON
ST
he c
ost
for
7 da
nce
less
ons
is $
82.T
he c
ost
for
11 le
sson
s is
$12
2.W
rite
a li
near
equ
atio
n to
fin
d th
e to
tal c
ost
Cfo
r !
less
ons.
The
n us
e th
e eq
uati
on t
ofi
nd t
he c
ost
of 4
less
ons.
C#
10!
%12
;$52
21.W
EATH
ERIt
is 7
6°F
at
the
6000
-foo
t le
vel o
f a
mou
ntai
n,an
d 49
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t th
e 12
,000
-foo
tle
vel o
f th
e m
ount
ain.
Wri
te a
line
ar e
quat
ion
to f
ind
the
tem
pera
ture
Tat
an
elev
atio
ne
on t
he m
ount
ain,
whe
re e
is in
tho
usan
ds o
f fe
et.
T#
!4.
5e%
103
3 " 41 " 25 " 2
1 " 41 " 4
9 " 23 " 2
2 " 5
1 " 34 " 3
1 " 4
( –3,
1)
( –1,
–3)
x
y
O( 0
, 5)
( 4, 1
) x
y
O
( 4, –
2)
( 2, –
4)
xy
O
7 " 23 " 2
1 " 2
3 # 21 # 2
( –1,
–3)
x
y
O
m !
–1
( –2,
2)
x
y O
m !
–2
( 1, 2
)
x
y
Om
! 3
Pra
ctic
e (A
vera
ge)
Wri
ting
Equ
atio
ns in
Slo
pe-In
terc
ept F
orm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-4
5-4
Answers (Lesson 5-4)
© Glencoe/McGraw-Hill A13 Glencoe Algebra 1
Ans
wer
s
Rea
din
g t
o L
earn
Math
emati
csW
ritin
g E
quat
ions
in S
lope
-Inte
rcep
t Fo
rm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-4
5-4
©G
lenc
oe/M
cGra
w-H
ill30
3G
lenc
oe A
lgeb
ra 1
Lesson 5-4
Pre-
Act
ivit
yH
ow c
an s
lop
e-in
terc
ept
form
be
use
d t
o m
ake
pre
dic
tion
s?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 5-
4 at
the
top
of
page
280
in y
our
text
book
.
•W
hat
is t
he r
ate
of c
hang
e pe
r ye
ar?
abou
t 20
00 p
er y
ear
•St
udy
the
patt
ern
on t
he g
raph
.How
wou
ld y
ou f
ind
the
popu
lati
on in
1997
?A
dd 2
000
to t
he 1
996
popu
latio
n,w
hich
giv
es 1
79,0
00.
Read
ing
the
Less
on
1.Su
ppos
e yo
u ar
e gi
ven
that
a li
ne g
oes
thro
ugh
(2,5
) an
d ha
s a
slop
e of
!2.
Use
thi
sin
form
atio
n to
com
plet
e th
e fo
llow
ing
equa
tion
.
y"
⎯⎯
mx
⎯⎯
#b
↓↓
"$
#
2.W
hat
mus
t yo
u fi
rst
do if
you
are
not
giv
en t
he s
lope
in t
he p
robl
em?
Use
the
info
rmat
ion
give
n (t
wo
poin
ts)
to f
ind
the
slop
e.
3.W
hat
is t
he f
irst
ste
p in
ans
wer
ing
any
stan
dard
ized
tes
t pr
acti
ce q
uest
ion?
Rea
d th
e pr
oble
m.
4.W
hat
are
four
ste
ps y
ou c
an u
se in
sol
ving
a w
ord
prob
lem
?
Exp
lore
,Pla
n,S
olve
,Exa
min
e
5.D
efin
e th
e te
rm li
near
ext
rapo
lati
on.
Line
ar e
xtra
pola
tion
mea
ns u
sing
a li
near
equ
atio
n to
pre
dict
val
ues
that
are
outs
ide
the
two
give
n da
ta p
oint
s.
Hel
ping
You
Rem
embe
r
6.In
you
r ow
n w
ords
,exp
lain
how
you
wou
ld a
nsw
er a
que
stio
n th
at a
sks
you
to w
rite
th
e sl
ope-
inte
rcep
t fo
rm o
f an
equ
atio
n.S
ampl
e an
swer
:Det
erm
ine
wha
tin
form
atio
n yo
u ar
e gi
ven.
If yo
u ha
ve a
poi
nt a
nd t
he s
lope
,you
can
subs
titut
e th
e x-
and
y-v
alue
s an
d th
e sl
ope
into
y!
mx
"b
to f
ind
the
valu
e of
b.T
hen
use
the
valu
es o
f m
and
bto
wri
te t
he e
quat
ion.
If yo
uha
ve t
wo
poin
ts,u
se t
hem
to
find
the
slop
e,an
d th
en u
se t
he m
etho
d fo
ra
poin
t an
d th
e sl
ope.
b2
#2
5
©G
lenc
oe/M
cGra
w-H
ill30
4G
lenc
oe A
lgeb
ra 1
Cel
sius
and
Kel
vin
Tem
pera
ture
sIf
you
blo
w u
p a
ballo
on a
nd p
ut it
in t
he r
efri
gera
tor,
the
ballo
on w
ill
shri
nk a
s th
e te
mpe
ratu
re o
f th
e ai
r in
the
bal
loon
dec
reas
es.
The
vol
ume
of a
cer
tain
gas
is m
easu
red
at 3
0°C
elsi
us.T
he
tem
pera
ture
is d
ecre
ased
and
the
vol
ume
is m
easu
red
agai
n.
1.G
raph
thi
s ta
ble
on t
he c
oord
inat
e pl
ane
prov
ided
bel
ow.
2.F
ind
the
equa
tion
of
the
line
that
pas
ses
thro
ugh
the
poin
ts y
ou
grap
hed
in E
xerc
ise
1.
v!
t"
182
3.U
se t
he e
quat
ion
you
foun
d in
Exe
rcis
e 2
to f
ind
the
tem
pera
ture
th
at w
ould
giv
e a
volu
me
of z
ero.
Thi
s te
mpe
ratu
re is
the
low
est
one
poss
ible
and
is c
alle
d ab
solu
te z
ero.
#27
3$C
4.In
184
8,L
ord
Kel
vin
prop
osed
a n
ew t
empe
ratu
re s
cale
wit
h 0
bein
g as
sign
ed t
o ab
solu
te z
ero.
The
siz
e of
the
deg
ree
chos
en w
as
the
sam
e si
ze a
s th
e C
elsi
us d
egre
e.C
hang
e ea
ch o
f th
e C
elsi
us
tem
pera
ture
s in
the
tab
le a
bove
to
degr
ees
Kel
vin.
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En
rich
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t
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ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-4
5-4
Answers (Lesson 5-4)
© Glencoe/McGraw-Hill A14 Glencoe Algebra 1
Stu
dy
Gu
ide
and I
nte
rven
tion
Wri
ting
Equ
atio
ns in
Poi
nt-S
lope
For
m
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-5
5-5
©G
lenc
oe/M
cGra
w-H
ill30
5G
lenc
oe A
lgeb
ra 1
Lesson 5-5
Poin
t-Sl
ope
Form
Poi
nt-S
lope
For
my
"y 1
!m
(x"
x 1),
whe
re (
x 1, y
1) is
a g
iven
poi
nt o
n a
nonv
ertic
al li
ne
and
mis
the
slop
e of
the
line
Wri
te t
he
poi
nt-
slop
e fo
rmof
an
equ
atio
n f
or a
lin
e th
at p
asse
s th
rou
gh (
6,1)
an
d h
as a
slo
pe
of !
.
y"
y 1!
m(x
"x 1
)P
oint
-slo
pe fo
rm
y"
1 !
"(x
"6)
m!
"; (
x 1, y
1) !
(6, 1
)
The
refo
re,t
he e
quat
ion
is y
"1!
"(x
"6)
.5 # 2
5 # 25 # 2
5 " 2
Wri
te t
he
poi
nt-
slop
efo
rm o
f an
equ
atio
n f
or a
hor
izon
tal
lin
e th
at p
asse
s th
rou
gh (
4,!
1).
y"
y 1!
m(x
"x 1
)P
oint
-slo
pe fo
rm
y"
("1)
!0(
x"
4)m
!0;
(x 1
, y1)
!(4
, "1)
y%
1 !
0S
impl
ify.
The
refo
re,t
he e
quat
ion
is y
%1
!0.
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Wri
te t
he
poi
nt-
slop
e fo
rm o
f an
equ
atio
n f
or a
lin
e th
at p
asse
s th
rou
gh e
ach
poi
nt
wit
h t
he
give
n s
lop
e.
1.2.
3.
y!
1#x
!4
y!
2 #
0y
%3
#!
2(x
!2)
4.(2
,1),
m!
45.
("7,
2),m
!6
6.(8
,3),
m!
1
y!
1 #
4(x
!2)
y!
2 #
6(x
%7)
y!
3#x
! 8
7.("
6,7)
,m!
08.
(4,9
),m
!9.
("4,
"5)
,m!
"
y!
7 #
0y
!9
#(x
!4)
y%
5#!
(x%
4)
10.W
rite
the
poi
nt-s
lope
for
m o
f an
equ
atio
n fo
r th
e ho
rizo
ntal
line
tha
t pa
sses
th
roug
h (4
,"2)
.y
%2
#0
11.W
rite
the
poi
nt-s
lope
for
m o
f an
equ
atio
n fo
r th
e ho
rizo
ntal
line
tha
t pa
sses
th
roug
h ("
5,6)
.y
!6
#0
12.W
rite
the
poi
nt-s
lope
for
m o
f an
equ
atio
n fo
r th
e ho
rizo
ntal
line
tha
t pa
sses
th
roug
h (5
,0).
y#
0
1 " 23 " 4
1 # 23 # 4
( 2, –
3)
x
y
O
m !
–2
( –3,
2)
x
y
O
m !
0( 4
, 1)
x
y
O
m !
1
©G
lenc
oe/M
cGra
w-H
ill30
6G
lenc
oe A
lgeb
ra 1
Form
s of
Lin
ear
Equa
tion
s
Slo
pe-In
terc
ept
Form
y!
mx
%b
m!
slop
e; b
!y-
inte
rcep
t
Poi
nt-S
lope
Fo
rmy
"y 1
!m
(x"
x 1)
m!
slop
e; (
x 1, y
1) is
a g
iven
poi
nt.
Sta
ndar
d A
x%
By
!C
Aan
d B
are
not b
oth
zero
. Usu
ally
Ais
non
nega
tive
and
A, B
, and
CFo
rmar
e in
tege
rs w
hose
gre
ates
t com
mon
fact
or is
1.
Stu
dy
Gu
ide
and I
nte
rven
tion
(c
onti
nued
)
Wri
ting
Equ
atio
ns in
Poi
nt-S
lope
For
m
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-5
5-5
Wri
te y
%5
#(x
!6)
in
stan
dar
d f
orm
.
y%
5 !
(x"
6)O
rigin
al e
quat
ion
3(y
%5)
!3 !
"(x"
6)M
ultip
ly e
ach
side
by
3.
3y%
15 !
2(x
"6)
Dis
trib
utiv
e P
rope
rty
3y%
15 !
2x"
12D
istr
ibut
ive
Pro
pert
y
3y!
2x"
27S
ubtr
act 1
5 fr
om e
ach
side
.
"2x
%3y
!"
27A
dd "
2xto
eac
h si
de.
2x"
3y!
27M
ultip
ly e
ach
side
by
"1.
The
refo
re,t
he s
tand
ard
form
of
the
equa
tion
is 2
x"
3y!
27.2 # 3
2 # 3
2 " 3W
rite
y!
2 #
!(x
!8)
in s
lop
e-in
terc
ept
form
.
y"
2 !
"(x
"8)
Orig
inal
equ
atio
n
y"
2 !
"x
%2
Dis
trib
utiv
e P
rope
rty
y!
"x
%4
Add
2 to
eac
h si
de.
The
refo
re,t
he s
lope
-int
erce
pt f
orm
of
the
equa
tion
is y
!"
x%
4.1 # 4
1 # 41 # 41 # 4
1 " 4Ex
ampl
e1Ex
ampl
e1Ex
ampl
e2Ex
ampl
e2
Wri
te e
ach
equ
atio
n i
n s
tan
dar
d f
orm
.
1.y
%2
!"
3(x
"1)
2.y
"1
!"
(x"
6)3.
y%
2 !
(x"
9)
3x%
y#
1x
%3y
#9
2x!
3y#
24
4.y
%3
!"
(x"
5)5.
y"
4 !
(x%
3)6.
y%
4 !
"(x
"1)
x%
y#
25x
!3y
#!
272x
%5y
#!
18
Wri
te e
ach
equ
atio
n i
n s
lop
e-in
terc
ept
form
.
7.y
%4
!4(
x"
2)8.
y"
5 !
(x"
6)9.
y"
8 !
"(x
%8)
y#
4x!
12y
#x
%3
y#
!x
%6
10.y
"6
!3 !x
""
11.y
%4
!"
2(x
%5)
12.y
%!
(x"
2)
y#
3x%
5y
#!
2x!
14y
#x
!8 " 3
1 " 2
1 # 25 # 3
1 # 3
1 " 41 " 3
1 # 41 # 3
2 # 55 # 3
2 # 31 # 3
Exer
cises
Exer
cises
Answers (Lesson 5-5)
© Glencoe/McGraw-Hill A15 Glencoe Algebra 1
Ans
wer
s
Skil
ls P
ract
ice
Wri
ting
Equ
atio
ns in
Poi
nt-S
lope
For
m
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-5
5-5
©G
lenc
oe/M
cGra
w-H
ill30
7G
lenc
oe A
lgeb
ra 1
Lesson 5-5
Wri
te t
he
poi
nt-
slop
e fo
rm o
f an
equ
atio
n f
or a
lin
e th
at p
asse
s th
rou
gh e
ach
poi
nt
wit
h t
he
give
n s
lop
e.
1.2.
3.
y%
2 #
3(x
%1)
y%
2 #
!(x
!1)
y%
3 #
0
4.(3
,1),
m!
05.
("4,
6),m
!8
6.(1
,"3)
,m!
"4
y!
1 #
0y
!6
#8(
x%
4)y
%3
#!
4(x
!1)
7.(4
,"6)
,m!
18.
(3,3
),m
!9.
("5,
"1)
,m!
"
y%
6 #
x!
4y
!3
#(x
!3)
y%
1 #
!(x
%5)
Wri
te e
ach
equ
atio
n i
n s
tan
dar
d f
orm
.
10.y
%1
!x
%2
11.y
%9
!"
3(x
"2)
12.y
"7
!4(
x%
4)
x!
y#
!1
3x%
y#
!3
4x!
y#
!23
13.y
"4
!"
(x"
1)14
.y"
6 !
4(x
%3)
15.y
%5
!"
5(x
"3)
x%
y#
54x
!y
#!
185x
%y
#10
16.y
"10
!"
2(x
"3)
17.y
"2
!"
(x"
4)18
.y%
11 !
(x%
3)
2x%
y#
16x
%2y
#8
x!
3y#
30
Wri
te e
ach
equ
atio
n i
n s
lop
e-in
terc
ept
form
.
19.y
"4
!3(
x"
2)20
.y%
2 !
"(x
%4)
21.y
"6
!"
2(x
%2)
y#
3x!
2y
#!
x!
6y
#!
2x%
2
22.y
%1
!"
5(x
"3)
23.y
"3
!6(
x"
1)24
.y"
8 !
3(x
%5)
y#
!5x
%14
y#
6x!
3y
#3x
%23
25.y
"2
!(x
%6)
26.y
%1
!"
(x%
9)27
.y"
!x
%
y#
x%
5y
#!
x!
4y
#x
%1
1 " 31 " 2
1 # 21 # 2
1 # 31 # 2
1 # 31 # 2
5 " 44 " 3
5 # 44 # 3
( 2, –
3)
x
y O
m !
0
( 1, –
2)x
y O
m !
–1
( –1,
–2)
x
y
O
m !
3
©G
lenc
oe/M
cGra
w-H
ill30
8G
lenc
oe A
lgeb
ra 1
Wri
te t
he
poi
nt-
slop
e fo
rm o
f an
equ
atio
n f
or a
lin
e th
at p
asse
s th
rou
gh e
ach
poi
nt
wit
h t
he
give
n s
lop
e.
1.(2
,2),
m!
"3
2.(1
,"6)
,m!
"1
3.("
3,"
4),m
!0
y!
2 #
!3(
x!
2)y
%6
#!
(x!
1)y
%4
#0
4.(1
,3),
m!
"5.
("8,
5),m
!"
6.(3
,"3)
,m!
y!
3 #
!(x
!1)
y!
5 #
!(x
%8)
y%
3 #
(x!
3)
Wri
te e
ach
equ
atio
n i
n s
tan
dar
d f
orm
.
7.y
"11
!3(
x"
2)8.
y"
10 !
"(x
"2)
9.y
%7
!2(
x%
5)3x
!y
#!
5x
%y
#12
2x!
y#
!3
10.y
"5
!(x
%4)
11.y
%2
!"
(x%
1)12
.y"
6 !
(x"
3)
3x!
2y#
!22
3x%
4y#
!11
4x!
3y#
!6
13.y
%4
!1.
5(x
%2)
14.y
"3
!"
2.4(
x"
5)15
.y"
4 !
2.5(
x%
3)3x
!2y
#2
12x
%5y
#75
5x!
2y#
!23
Wri
te e
ach
equ
atio
n i
n s
lop
e-in
terc
ept
form
.
16.y
%2
!4(
x%
2)17
.y%
1 !
"7(
x%
1)18
.y"
3 !
"5(
x%
12)
y#
4x%
6y
#!
7x!
8y
#!
5x!
57
19.y
"5
!(x
%4)
20.y
"!
"3 !x
%"
21.y
"!
"2 !x
""
y#
x%
11y
#!
3x!
y#
!2x
%
CO
NST
RU
CTI
ON
For
Exe
rcis
es 2
2–24
,use
th
e fo
llow
ing
info
rmat
ion
.A
con
stru
ctio
n co
mpa
ny c
harg
es $
15 p
er h
our
for
debr
is r
emov
al,p
lus
a on
e-ti
me
fee
for
the
use
of a
tra
sh d
umps
ter.
The
tot
al f
ee f
or 9
hou
rs o
f se
rvic
e is
$19
5.
22.W
rite
the
poi
nt-s
lope
form
of a
n eq
uati
on t
o fin
d th
e to
tal f
ee y
for
any
num
ber
of h
ours
x.
y!
195
#15
(x!
9)23
.Wri
te t
he e
quat
ion
in s
lope
-int
erce
pt f
orm
.y
#15
x%
6024
.Wha
t is
the
fee
for
the
use
of
a tr
ash
dum
pste
r?$6
0
MO
VIN
GF
or E
xerc
ises
25–
27,u
se t
he
foll
owin
g in
form
atio
n.
The
re is
a s
et d
aily
fee
for
rent
ing
a m
ovin
g tr
uck,
plus
a c
harg
e of
$0.
50 p
er m
ile d
rive
n.It
cos
ts $
64 t
o re
nt t
he t
ruck
on
a da
y w
hen
it is
dri
ven
48 m
iles.
25.W
rite
the
poi
nt-s
lope
for
m o
f an
equ
atio
n to
fin
d th
e to
tal c
harg
e y
for
any
num
ber
ofm
iles
xfo
r a
one-
day
rent
al.
y!
64 #
0.5(
x!
48)
26.W
rite
the
equ
atio
n in
slo
pe-i
nter
cept
for
m.
y#
0.5x
%40
27.W
hat
is t
he d
aily
fee
?$4
0
7 " 61 " 2
3 " 2
1 # 42 # 3
1 # 41 # 4
3 # 2
4 # 33 # 4
3 # 2
1 " 32 " 5
3 " 4
1 # 32 # 5
3 # 4
Pra
ctic
e (A
vera
ge)
Wri
ting
Equ
atio
ns in
Poi
nt-S
lope
For
m
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-5
5-5
Answers (Lesson 5-5)
© Glencoe/McGraw-Hill A16 Glencoe Algebra 1
Rea
din
g t
o L
earn
Math
emati
csW
ritin
g E
quat
ions
in P
oint
-Slo
pe F
orm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-5
5-5
©G
lenc
oe/M
cGra
w-H
ill30
9G
lenc
oe A
lgeb
ra 1
Lesson 5-5
Pre-
Act
ivit
yH
ow c
an y
ou u
se t
he
slop
e fo
rmu
la t
o w
rite
an
equ
atio
n o
f a
lin
e?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 5-
5 at
the
top
of
page
286
in y
our
text
book
.
Not
e th
at in
the
fin
al e
quat
ion
ther
e is
a v
alue
sub
trac
ted
from
xan
d fr
om y
.Wha
t ar
e th
ese
valu
es?
The
valu
e su
btra
cted
fro
m x
is t
he x
-coo
rdin
ate
of t
he g
iven
poin
t.Th
e va
lue
subt
ract
ed f
rom
yis
the
y-c
oord
inat
e of
the
give
n po
int.
Read
ing
the
Less
on
1.In
the
for
mul
a y
!y 1
"m
(x!
x 1),
wha
t do
x1
and
y 1re
pres
ent?
x 1an
d y 1
repr
esen
t th
e co
ordi
nate
s of
any
giv
en p
oint
on
the
grap
h of
the
line
.
2.C
ompl
ete
the
char
t be
low
by
listi
ng t
hree
for
ms
of e
quat
ions
.The
n w
rite
the
for
mul
a fo
rea
ch f
orm
.Fin
ally
,wri
te t
hree
exa
mpl
es o
f eq
uati
ons
in t
hose
for
ms.
Sam
ple
exam
ples
are
giv
en.
Form
of
Equ
atio
nFo
rmul
aE
xam
ple
slop
e-in
terc
ept
y!
mx
"b
y!
3x"
2
poin
t-sl
ope
y#
y 1!
m(x
#x 1
)y
#2
!4(
x"
3)
stan
dard
Ax
"B
y!
C3x
#5y
!15
3.R
efer
to
Exa
mpl
e 5
on p
age
288
of y
our
text
book
.Wha
t do
you
thi
nk t
he h
ypot
enus
eof
ari
ght
tria
ngle
is?
Sam
ple
answ
ers:
The
hypo
tenu
se is
the
long
est
side
of
the
righ
t tr
iang
le.T
he h
ypot
enus
e is
the
sid
e op
posi
te t
he r
ight
ang
le in
a ri
ght
tria
ngle
.
Hel
ping
You
Rem
embe
r
4.Su
ppos
e yo
u co
uld
not
rem
embe
r al
l thr
ee f
orm
ulas
list
ed in
the
tab
le a
bove
.Whi
ch o
fth
e fo
rms
wou
ld y
ou c
once
ntra
te o
n fo
r w
riti
ng li
near
equ
atio
ns?
Exp
lain
why
you
cho
seth
at f
orm
.S
ampl
e an
swer
:Poi
nt-s
lope
form
;the
slo
pe-in
terc
ept
form
ca
n be
wri
tten
fro
m t
he p
oint
-slo
pe fo
rm.T
his
is s
o be
caus
e th
e y-
inte
rcep
t le
ts y
ou w
rite
the
coo
rdin
ates
of
the
poin
t w
here
the
line
cros
ses
the
y-ax
is.Y
ou c
an u
se t
hat
poin
t as
the
giv
en p
oint
in t
he
poin
t-sl
ope
form
ula.
©G
lenc
oe/M
cGra
w-H
ill31
0G
lenc
oe A
lgeb
ra 1
Col
linea
rity
Yo
u ha
ve le
arne
d ho
w t
o fi
nd t
he s
lope
bet
wee
n tw
o po
ints
on
a lin
e.D
oes
it m
atte
r w
hich
tw
o po
ints
you
use
? H
ow d
oes
your
cho
ice
of p
oint
s af
fect
the
slop
e-in
terc
ept
form
of
the
equa
tion
of
the
line?
1.C
hoos
e th
ree
diff
eren
t pa
irs
of p
oint
s fr
om t
he g
raph
at
the
righ
t.W
rite
the
slo
pe-i
nter
cept
for
m o
f th
e lin
e us
ing
each
pai
r.
y!
1x"
1
2.H
ow a
re t
he e
quat
ions
rel
ated
?
They
are
the
sam
e.
3.W
hat
conc
lusi
on c
an y
ou d
raw
fro
m y
our
answ
ers
to E
xerc
ises
1 a
nd 2
?
The
equa
tion
of a
line
is t
he s
ame
no m
atte
r w
hich
tw
o po
ints
yo
u ch
oose
.
Whe
n po
ints
are
con
tain
ed in
the
sam
e lin
e,th
ey a
re s
aid
to b
e co
llin
ear.
Eve
n th
ough
poi
nts
may
look
like
they
form
a s
trai
ght
line
whe
n co
nnec
ted,
it d
oes
not
mea
n th
at t
hey
actu
ally
do.
By
chec
king
pai
rs o
f poi
nts
on a
lin
e yo
u ca
n de
term
ine
whe
ther
the
line
rep
rese
nts
a lin
ear
rela
tion
ship
.
4.C
hoos
e se
vera
l pai
rs o
f po
ints
fro
m t
he g
raph
at
the
righ
t an
d w
rite
the
slo
pe-i
nter
cept
for
m o
f th
e lin
e us
ing
each
pai
r.
y!
1x"
0;y
!2x
#2;
y!
2x"
1
5.W
hat
conc
lusi
on c
an y
ou d
raw
fro
m y
our
equa
tion
s in
E
xerc
ise
4? I
s th
is a
str
aigh
t lin
e?
The
poin
ts a
re n
ot c
ollin
ear.
This
is n
ot a
st
raig
ht li
ne.
x
y O
x
y
O
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-5
5-5
Answers (Lesson 5-5)
© Glencoe/McGraw-Hill A17 Glencoe Algebra 1
Ans
wer
s
Stu
dy
Gu
ide
and I
nte
rven
tion
Geo
met
ry:P
aral
lel a
nd P
erpe
ndic
ular
Lin
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-6
5-6
©G
lenc
oe/M
cGra
w-H
ill31
1G
lenc
oe A
lgeb
ra 1
Lesson 5-6
Para
llel L
ines
Tw
o no
nver
tica
llin
es a
re p
aral
leli
f th
ey h
ave
the
sam
e sl
ope.
All
vert
ical
line
s ar
e pa
ralle
l.
Wri
te t
he
slop
e-in
terc
ept
form
for
an
equ
atio
n o
f th
e li
ne
that
pas
ses
thro
ugh
(!
1,6)
an
d i
s p
aral
lel
to t
he
grap
h o
f y
#2x
%12
.
A li
ne p
aral
lel t
o y
!2x
%12
has
the
sam
e sl
ope,
2.R
epla
ce m
wit
h 2
and
(x1,
y 1)
wit
h ("
1,6)
in t
he p
oint
-slo
pe f
orm
.y
"y 1
!m
(x"
x 1)
Poi
nt-s
lope
form
y"
6 !
2(x
"("
1))
m!
2; (
x 1, y
1) !
("1,
6)
y"
6 !
2(x
%1)
Sim
plify
.
y"
6 !
2x%
2D
istr
ibut
ive
Pro
pert
y
y!
2x%
8S
lope
-inte
rcep
t for
m
The
refo
re,t
he e
quat
ion
is y
!2x
%8.
Wri
te t
he
slop
e-in
terc
ept
form
for
an
equ
atio
n o
f th
e li
ne
that
pas
ses
thro
ugh
th
egi
ven
poi
nt
and
is
par
alle
l to
th
e gr
aph
of
each
equ
atio
n.
1.2.
3.
y#
x!
4y
#!
x%
3y
#x
%7
4.("
2,2)
,y!
4x"
25.
(6,4
),y
!x
%1
6.(4
,"2)
,y!
"2x
%3
y#
4x%
10y
#x
%2
y#
!2x
%6
7.("
2,4)
,y!
"3x
%10
8.("
1,6)
,3x
%y
!12
9.(4
,"6)
,x%
2y!
5
y#
!3x
!2
y#
!3x
%3
y#
!x
!4
10.F
ind
an e
quat
ion
of t
he li
ne t
hat
has
a y-
inte
rcep
t of
2 t
hat
is p
aral
lel t
o th
e gr
aph
ofth
e lin
e 4x
%2y
!8.
y#
!2x
%2
11.F
ind
an e
quat
ion
of t
he li
ne t
hat
has
a y-
inte
rcep
t of
"1
that
is p
aral
lel t
o th
e gr
aph
ofth
e lin
e x
"3y
!6.
y#
x!
1
12.F
ind
an e
quat
ion
of t
he li
ne t
hat
has
a y-
inte
rcep
t of
"4
that
is p
aral
lel t
o th
e gr
aph
ofth
e lin
e y
!6.
y#
!4
1 " 3
1 " 2
1 " 3
1 # 3
4 " 31 " 2
( –3,
3)
x
y
O
4x "
3y
! –
12
( –8,
7)
x
y
O
y !
–1 2x
" 4
2
2
( 5, 1
)x
y
O
y !
x "
8
Exam
ple
Exam
ple
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill31
2G
lenc
oe A
lgeb
ra 1
Perp
endi
cula
r Li
nes
Tw
o lin
es a
re p
erp
end
icu
lar
if t
heir
slo
pes
are
nega
tive
reci
proc
als
of e
ach
othe
r.V
erti
cal a
nd h
oriz
onta
l lin
es a
re p
erpe
ndic
ular
.
Wri
te t
he
slop
e-in
terc
ept
form
for
an
equ
atio
n t
hat
pas
ses
thro
ugh
(!4,
2) a
nd
is
per
pen
dic
ula
r to
th
e gr
aph
of
2x!
3y#
9.
Fin
d th
e sl
ope
of 2
x"
3y!
9.2x
"3y
!9
Orig
inal
equ
atio
n"
3y!
"2x
%9
Sub
trac
t 2x
from
eac
h si
de.
y!
x"
3D
ivid
e ea
ch s
ide
by "
3.
The
slo
pe o
f y!
x"
3 is
.S
o,th
e sl
ope
of t
he li
ne p
assi
ng t
hrou
gh ("
4,2)
tha
t is
2 # 3
2 # 3
2 # 3Stu
dy
Gu
ide
and I
nte
rven
tion
(c
onti
nued
)
Geo
met
ry:P
aral
lel a
nd P
erpe
ndic
ular
Lin
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-6
5-6
Exam
ple
Exam
ple
Exer
cises
Exer
cises
perp
endi
cula
r to
thi
s lin
e is
the
neg
ativ
e re
cipr
ocal
of
,or
".
Use
the
poi
nt-s
lope
for
m t
o fi
nd t
he e
quat
ion.
y"
y 1!
m(x
"x 1
)P
oint
-slo
pe fo
rm
y"
2 !
"(x
"("
4))
m!
"; (
x 1, y
1) !
("4,
2)
y"
2 !
"(x
%4)
Sim
plify
.
y"
2 !
"x
"6
Dis
trib
utiv
e P
rope
rty
y!
"x
"4
Slo
pe-in
terc
ept f
orm
Wri
te t
he
slop
e-in
terc
ept
form
for
an
equ
atio
n o
f th
e li
ne
that
pas
ses
thro
ugh
th
egi
ven
poi
nt
and
is
per
pen
dic
ula
r to
th
e gr
aph
of
each
equ
atio
n.
1.(4
,2),
y!
x%
12.
(2,"
3),y
!"
x%
43.
(6,4
),y
!7x
%1
y#
!2x
%10
y#
x!
6y
#!
x%
4.("
8,"
7),y
!"
x"
85.
(6,"
2),y
!"
3x"
66.
("5,
"1)
,y!
x"
3
y#
x%
1y
#x
!4
y#
!x
!3
7.("
9,"
5),y
!"
3x"
18.
("1,
3),2
x%
4y!
129.
(6,"
6),3
x"
y!
6
y#
x!
2y
#2x
%5
y#
!x
!4
10.F
ind
an e
quat
ion
of t
he li
ne t
hat
has
a y-
inte
rcep
t of
"2
and
is p
erpe
ndic
ular
to
the
grap
h of
the
line
x"
2y!
5.y
#!
2x!
2
11.F
ind
an e
quat
ion
of t
he li
ne t
hat
has
a y-
inte
rcep
t of
5 a
nd is
per
pend
icul
ar t
o th
e gr
aph
of t
he li
ne 4
x%
3y!
8.y
#x
%5
3 " 4
1 " 31 " 3
2 " 51 " 3
5 # 234 " 71 " 7
3 " 2
2 # 31 # 2
3 # 23 # 23 # 2
3 # 23 # 2
3 # 22 # 3
Answers (Lesson 5-6)
© Glencoe/McGraw-Hill A18 Glencoe Algebra 1
Skil
ls P
ract
ice
Geo
met
ry:P
aral
lel a
nd P
erpe
ndic
ular
Lin
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-6
5-6
©G
lenc
oe/M
cGra
w-H
ill31
3G
lenc
oe A
lgeb
ra 1
Lesson 5-6
Wri
te t
he
slop
e-in
terc
ept
form
of
an e
quat
ion
of
the
lin
e th
at p
asse
s th
rou
gh t
he
give
n p
oin
t an
d i
s p
aral
lel
to t
he
grap
h o
f ea
ch e
quat
ion
.
1.2.
3.
y#
2x%
1y
#!
xy
#x
%3
4.(3
,2),
y!
3x%
45.
("1,
"2)
,y!
"3x
%5
6.("
1,1)
,y!
x"
4
y#
3x!
7y
#!
3x!
5y
#x
%2
7.(1
,"3)
,y!
"4x
"1
8.("
4,2)
,y!
x%
39.
("4,
3),y
!x
"6
y#
!4x
%1
y#
x%
6y
#x
%5
10.(
4,1)
,y!
"x
%7
11.(
"5,
"1)
,2y
!2x
"4
12.(
3,"
1),3
y!
x%
9
y#
!x
%2
y#
x%
4y
#x
!2
Wri
te t
he
slop
e-in
terc
ept
form
of
an e
quat
ion
of
the
lin
e th
at p
asse
s th
rou
gh t
he
give
n p
oin
t an
d i
s p
erp
end
icu
lar
to t
he
grap
h o
f ea
ch e
quat
ion
.
13.(
"3,
"2)
,y!
x%
214
.(4,
"1)
,y!
2x"
415
.("
1,"
6),x
%3y
!6
y#
!x
!5
y#
!x
%1
y#
3x!
3
16.(
"4,
5),y
!"
4x"
117
.("
2,3)
,y!
x"
418
.(0,
0),y
!x
"1
y#
x%
6y
#!
4x!
5y
#!
2x
19.(
3,"
3),y
!x
%5
20.(
"5,
1),y
!"
x"
721
.(0,
"2)
,y!
"7x
%3
y#
!x
%1
y#
x%
4y
#x
!2
22.(
2,3)
,2x
%10
y!
323
.("
2,2)
,6x
%3y
!"
924
.("
4,"
3),8
x"
2y!
16
y#
5x!
7y
#x
%3
y#
!x
!4
1 " 41 " 2
1 " 73 " 5
4 " 3
5 # 33 # 4
1 " 4
1 # 21 # 4
1 " 2
1 " 31 " 4
1 # 4
1 " 2
1 # 2
1 " 2
( –2,
2)
x
y O
y !
1 2x %
1( 1
, –1)
x
y
O
y !
–x
% 3
( –2,
–3)
x
y O
y !
2x
" 1
©G
lenc
oe/M
cGra
w-H
ill31
4G
lenc
oe A
lgeb
ra 1
Wri
te t
he
slop
e-in
terc
ept
form
of
an e
quat
ion
of
the
lin
e th
at p
asse
s th
rou
gh t
he
give
n p
oin
t an
d i
s p
aral
lel
to t
he
grap
h o
f ea
ch e
quat
ion
.
1.(3
,2),
y!
x%
52.
("2,
5),y
!"
4x%
23.
(4,"
6),y
!"
x%
1
y#
x!
1y
#!
4x!
3y
#!
x!
3
4.(5
,4),
y!
x"
25.
(12,
3),y
!x
%5
6.(3
,1),
2x%
y!
5
y#
x%
2y
#x
!13
y#
!2x
%7
7.("
3,4)
,3y
!2x
"3
8.("
1,"
2),3
x"
y!
59.
("8,
2),5
x"
4y!
1
y#
x%
6y
#3x
%1
y#
x%
12
10.(
"1,
"4)
,9x
%3y
!8
11.(
"5,
6),4
x%
3y!
112
.(3,
1),2
x%
5y!
7
y#
!3x
!7
y#
!x
!y
#!
x%
Wri
te t
he
slop
e-in
terc
ept
form
of
an e
quat
ion
of
the
lin
e th
at p
asse
s th
rou
gh t
he
give
n p
oin
t an
d i
s p
erp
end
icu
lar
to t
he
grap
h o
f ea
ch e
quat
ion
.
13.(
"2,
"2)
,y!
"x
%9
14.(
"6,
5),x
"y
!5
15.(
"4,
"3)
,4x
%y
!7
y#
3x%
4y
#!
x!
1y
#x
!2
16.(
0,1)
,x%
5y!
1517
.(2,
4),x
"6y
!2
18.(
"1,
"7)
,3x
%12
y!
"6
y#
5x%
1y
#!
6x%
16y
#4x
!3
19.(
"4,
1),4
x%
7y!
620
.(10
,5),
5x%
4y!
821
.(4,
"5)
,2x
"5y
!"
10
y#
x%
8y
#x
!3
y#
!x
%5
22.(
1,1)
,3x
%2y
!"
723
.("
6,"
5),4
x%
3y!
"6
24.(
"3,
5),5
x"
6y!
9
y#
x%
y#
x!
y#
!x
%
25.G
EOM
ETRY
Qua
drila
tera
l AB
CD
has
diag
onal
s A#
C#an
d B#
D#.
Det
erm
ine
whe
ther
A #C#
is p
erpe
ndic
ular
to
B#D#
.Exp
lain
.
Yes;
they
are
per
pend
icul
ar b
ecau
se t
heir
slo
pes
are
7 an
d !
,whi
ch a
re n
egat
ive
reci
proc
als.
26.G
EOM
ETRY
Tri
angl
e A
BC
has
vert
ices
A(0
,4),
B(1
,2),
and
C(4
,6).
Det
erm
ine
whe
ther
tri
angl
e A
BC
is a
rig
ht t
rian
gle.
Exp
lain
.
Yes;
side
s A!
B!an
d A!
C!ar
e pe
rpen
dicu
lar
beca
use
thei
r sl
opes
are
!2
and
,whi
ch a
re n
egat
ive
reci
proc
als.
1 " 2
1 " 7
x
y O
A
D
C
B
7 " 56 " 5
1 " 23 " 4
1 " 32 " 3
5 " 24 " 5
7 " 4
1 " 4
1 # 3
11 " 52 " 5
2 " 34 " 3
5 " 42 " 3
4 " 32 " 5
4 # 32 # 5
3 " 4
3 # 4
Pra
ctic
e (A
vera
ge)
Geo
met
ry:P
aral
lel a
nd P
erpe
ndic
ular
Lin
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-6
5-6
Answers (Lesson 5-6)
© Glencoe/McGraw-Hill A19 Glencoe Algebra 1
Ans
wer
s
Rea
din
g t
o L
earn
Math
emati
csG
eom
etry
:Par
alle
l and
Per
pend
icul
ar L
ines
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-6
5-6
©G
lenc
oe/M
cGra
w-H
ill31
5G
lenc
oe A
lgeb
ra 1
Lesson 5-6
Pre-
Act
ivit
yH
ow c
an y
ou d
eter
min
e w
het
her
tw
o li
nes
are
par
alle
l?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 5-
6 at
the
top
of
page
292
in y
our
text
book
.
•W
hat
is a
fam
ily o
f gr
aphs
?A
gro
up o
f gr
aphs
tha
t ha
ve a
t le
ast
one
char
acte
rist
ic in
com
mon
,suc
h as
slo
pe o
r y-
inte
rcep
t.
•D
o yo
u th
ink
lines
tha
t do
not
app
ear
to in
ters
ect
are
para
llel o
rpe
rpen
dicu
lar?
para
llel
Read
ing
the
Less
on
1.R
efer
to
the
Key
Con
cept
box
on
page
292
.Why
doe
s th
e de
fini
tion
use
the
ter
mno
nver
tica
lw
hen
talk
ing
abou
t lin
es w
ith
the
sam
e sl
ope?
Vert
ical
line
s ha
vesl
opes
tha
t ar
e un
defin
ed s
o w
e ca
nnot
say
the
y ha
ve t
he s
ame
slop
e.
2.W
hat
is a
rig
ht a
ngle
?S
ampl
e an
swer
s:A
rig
ht a
ngle
is o
ne t
hat
mea
sure
s90
°.It
is a
n an
gle
form
ed b
y pe
rpen
dicu
lar
lines
.
3.R
efer
to
the
Key
Con
cept
box
on
page
293
.Des
crib
e ho
w y
ou f
ind
the
oppo
site
rec
ipro
cal
of a
num
ber.
Sam
ple
answ
er:T
he r
ecip
roca
l of
a gi
ven
num
ber
is t
henu
mbe
r fo
rmed
whe
n yo
u sw
itch
the
num
erat
or a
nd d
enom
inat
or.T
hen
you
give
it t
he o
ppos
ite s
ign
of t
he o
rigi
nal n
umbe
r.
4.W
rite
the
opp
osit
e re
cipr
ocal
of
each
num
ber.
a.2
!b.
!3
c.!
d.!
5
Hel
ping
You
Rem
embe
r
5.O
ne w
ay t
o re
mem
ber
how
slo
pes
of p
aral
lel l
ines
are
rel
ated
is t
o sa
y “s
ame
dire
ctio
n,sa
me
slop
e.”T
ry t
o th
ink
of a
phr
ase
to h
elp
you
rem
embe
r th
at p
erpe
ndic
ular
line
sha
ve s
lope
s th
at a
re o
ppos
ite
reci
proc
als.
Sam
ple
answ
er:N
icel
y ri
ght
angl
es fo
rmed
,use
opp
osite
rec
ipro
cals
.
1 " 513 " 12
12 " 131 " 3
1 " 2
©G
lenc
oe/M
cGra
w-H
ill31
6G
lenc
oe A
lgeb
ra 1
Pen
cils
of
Line
sA
ll of
the
line
s th
at p
ass
thro
ugh
a si
ngle
poi
nt in
the
sam
e pl
ane
are
calle
d a
pen
cil o
f li
nes
.
All
lines
wit
h th
e sa
me
slop
e,bu
t di
ffer
ent
inte
rcep
ts,a
re a
lso
calle
d a
“pen
cil,”
a pe
nci
l of
para
llel
lin
es.
Gra
ph
som
e of
th
e li
nes
in
eac
h p
enci
l.
1.A
pen
cil o
f lin
es t
hrou
gh t
he
2.A
pen
cil o
f lin
es d
escr
ibed
by
poin
t (1
,3)
y!
4 #
m(x
!2)
,whe
re m
is a
ny
real
num
ber
3.A
pen
cil o
f lin
es p
aral
lel t
o th
e lin
e 4.
A p
enci
l of
lines
des
crib
ed b
y x
!2y
#7
y#
mx
$3m
!2
x
y
Ox
y
O
x
y
Ox
y
O
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-6
5-6
Answers (Lesson 5-6)
© Glencoe/McGraw-Hill A20 Glencoe Algebra 1
Stu
dy
Gu
ide
and I
nte
rven
tion
Sca
tter
Plo
ts a
nd L
ines
of F
it
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-7
5-7
©G
lenc
oe/M
cGra
w-H
ill31
7G
lenc
oe A
lgeb
ra 1
Lesson 5-7
Inte
rpre
t Po
ints
on
a Sc
atte
r Pl
otA
sca
tter
plo
tis
a g
raph
in w
hich
tw
o se
ts o
fda
ta a
re p
lott
ed a
s or
dere
d pa
irs
in a
coo
rdin
ate
plan
e.If
yin
crea
ses
as x
incr
ease
s,th
ere
isa
pos
itiv
e co
rrel
atio
nbe
twee
n x
and
y.If
yde
crea
ses
as x
incr
ease
s,th
ere
is a
neg
ativ
eco
rrel
atio
nbe
twee
n x
and
y.If
xan
d y
are
not
rela
ted,
ther
e is
no
corr
elat
ion
.
EARN
ING
ST
he
grap
h a
t th
e ri
ght
show
s th
e am
oun
t of
mon
ey C
arm
en e
arn
ed e
ach
wee
k an
d th
e am
oun
t sh
e de
posi
ted
in h
er s
avin
gsac
cou
nt
that
sam
e w
eek.
Det
erm
ine
wh
eth
er t
he
grap
h s
how
s a
pos
itiv
e co
rrel
atio
n,a
neg
ativ
eco
rrel
atio
n,o
r n
o co
rrel
atio
n.I
f th
ere
is a
p
osit
ive
or n
egat
ive
corr
elat
ion
,des
crib
e it
sm
ean
ing
in t
he
situ
atio
n.
The
gra
ph s
how
s a
posi
tive
cor
rela
tion
.The
mor
e C
arm
en e
arns
,the
mor
e sh
e sa
ves.
Det
erm
ine
wh
eth
er e
ach
gra
ph
sh
ows
a p
osit
ive
corr
elat
ion
,a n
egat
ive
corr
elat
ion
,or
no
corr
elat
ion
.If
ther
e is
a p
osit
ive
corr
elat
ion
,des
crib
e it
.
1.2.
no c
orre
latio
nN
egat
ive
corr
elat
ion;
as t
ime
in
crea
ses,
spee
d de
crea
ses.
3.4.
Pos
itive
cor
rela
tion;
as t
he
Pos
itive
cor
rela
tion;
as t
henu
mbe
r of
yea
rs in
crea
ses,
the
num
ber
of y
ears
incr
ease
s,th
enu
mbe
r of
clu
bs in
crea
ses.
num
ber
of f
unds
incr
ease
s.
Nu
mb
er o
f M
utu
al F
un
ds
Year
s Si
nce
1991
Number of Funds(thousands)
02
41
35
67
7 6 5 4 3
Sour
ce: T
he W
all S
treet
Jour
nal A
lman
ac
Gro
wth
of
Inve
stm
ent
Clu
bs
Year
s Si
nce
1990
Number of Clubs(thousands)
02
41
35
67
8
35 28 21 14 7
Sour
ce: T
he W
all S
treet
Jour
nal A
lman
ac
Ave
rag
e Jo
gg
ing
Sp
eed
Min
utes
Miles per Hour
010
205
1525
10 5
Ave
rag
e W
eekl
y W
ork
Ho
urs
in
U.S
.
Year
s Si
nce
1990
Hours
02
46
17
89
x
y
35
34.8
34.6
34.4
34.2
Sour
ce: T
he W
orld
Alm
anac
Car
men
’s E
arn
ing
s an
d S
avin
gs
Dol
lars
Ear
ned
Dollars Saved
040
8012
0
35 30 25 20 15 10 5
Exam
ple
Exam
ple
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill31
8G
lenc
oe A
lgeb
ra 1
Line
s of
Fit
Th
e ta
ble
belo
w s
how
s th
e n
um
ber
of s
tud
ents
per
com
pu
ter
inU
nit
ed S
tate
s p
ubl
ic s
choo
ls f
or c
erta
in s
choo
l ye
ars
from
199
0 to
200
0.
Year
1990
1992
1994
1996
1998
2000
Stu
dent
s pe
r C
ompu
ter
2218
1410
6.1
5.4
a.D
raw
a s
catt
er p
lot
and
det
erm
ine
wh
at
rela
tion
ship
exi
sts,
if a
ny.
Sinc
e y
decr
ease
s as
xin
crea
ses,
the
corr
elat
ion
is n
egat
ive.
b.D
raw
a l
ine
of f
it f
or t
he
scat
ter
plo
t.D
raw
a li
ne t
hat
pass
es c
lose
to
mos
t of
the
poin
ts.A
line
of
fit
is s
how
n.
c.W
rite
th
e sl
ope-
inte
rcep
t fo
rm o
f an
equ
atio
n f
or t
he
lin
e of
fit
.T
he li
ne o
f fi
t sh
own
pass
es t
hrou
gh
(199
3,16
) an
d (1
999,
5.7)
.Fin
d th
e sl
ope.
m!
m!
"1.
7
Fin
d b
in y
!"
1.7x
%b.
16 !
"1.
7 &
1993
%b
3404
!b
The
refo
re,a
n eq
uati
on o
f a
line
of f
it is
y!
"1.
7x%
3404
.
Ref
er t
o th
e ta
ble
for
Exe
rcis
es 1
–3.
1.D
raw
a s
catt
er p
lot.
3.W
rite
the
slo
pe-i
nter
cept
2.D
raw
a li
ne o
f fi
t fo
r th
e da
ta.
form
of
an e
quat
ion
for
the
line
of f
it.
The
poin
ts (
0,11
.43)
and
(2,1
2.28
) gi
ve
y#
0.42
5x%
11.4
3 as
a
line
of f
it.
U.S
. Pro
du
ctio
nW
ork
ers
Ho
url
y W
age
Year
s Si
nce
1995
Hourly Wage (dollars)
01
32
45
67
14 13 12 11
Sour
ce: T
he W
orld
Alm
anac
Year
sH
ourl
y S
ince
199
5 W
age
0$1
1.43
1$1
1.82
2$1
2.28
3$1
2.78
4$1
3.24
5.7
"16
##
1999
"19
93
Stu
den
ts p
er C
om
pu
ter
in U
.S. P
ub
lic
Sch
oo
ls
Year
Students per Computer
1990
1992
1994
1996
1998
2000
24 20 16 12 8 4 0
Sour
ce: T
he W
orld
Alm
anac
Stu
dy
Gu
ide
and I
nte
rven
tion
(c
onti
nued
)
Sca
tter
Plo
ts a
nd L
ines
of F
it
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-7
5-7
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 5-7)
© Glencoe/McGraw-Hill A21 Glencoe Algebra 1
Ans
wer
s
Skil
ls P
ract
ice
Sta
tistic
s:S
catt
er P
lots
and
Lin
es o
f Fit
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-7
5-7
©G
lenc
oe/M
cGra
w-H
ill31
9G
lenc
oe A
lgeb
ra 1
Lesson 5-7
Det
erm
ine
wh
eth
er e
ach
gra
ph
sh
ows
a po
siti
ve c
orre
lati
on,a
neg
ati
veco
rrel
ati
on,o
r n
o co
rrel
ati
on.I
f th
ere
is a
pos
itiv
e or
neg
ativ
e co
rrel
atio
n,
des
crib
e it
s m
ean
ing
in t
he
situ
atio
n.
1.2.
Pos
itive
;the
long
er t
he e
xerc
ise,
no c
orre
latio
nth
e m
ore
Cal
orie
s bu
rned
.3.
4.
Neg
ativ
e;as
wei
ght
incr
ease
s,N
egat
ive;
as t
he y
ear
incr
ease
s,th
e nu
mbe
r of
rep
etiti
ons
the
num
ber
of e
veni
ng
decr
ease
s.ne
wsp
aper
s de
crea
ses.
BASE
BALL
For
Exe
rcis
es 5
–7,u
se t
he
scat
ter
plo
t th
at s
how
s th
e av
erag
e p
rice
of
a m
ajor
-lea
gue
base
ball
tic
ket
fro
m 1
991
to 2
000.
5.D
eter
min
e w
hat
rela
tion
ship
,if
any,
exis
ts in
th
e da
ta.E
xpla
in.
Pos
itive
cor
rela
tion;
asth
e ye
ar in
crea
ses,
the
pric
e in
crea
ses.
6.U
se t
he p
oint
s (1
993,
9.60
) an
d (1
998,
13.6
0)
to w
rite
the
slo
pe-i
nter
cept
for
m o
f an
equ
atio
nfo
r th
e lin
e of
fit
sho
wn
in t
he s
catt
er p
lot.
y#
0.8x
!15
84.8
7.P
redi
ct t
he p
rice
of
a ti
cket
in 2
004.
abou
t $1
8.40
Bas
ebal
l Ti
cket
Pri
ces
Year
Average Price ($)
’91
’92
’93
’94
’95
’96
’97
’98
’99
18 16 14 12 10 8 0’0
0
Sour
ce: T
eam
Mar
ketin
g Re
port,
Chi
cago
Even
ing
New
spap
ers
Year
Number of Newspapers
’91
’92
’93
’94
’95
’96
’97
’98
’99
1050
1000 950
900
850
800
750 0
Sour
ce: E
dito
r & P
ublis
her
Wei
gh
t-Li
ftin
g
Wei
ght
(pou
nds)
Repetitions
040
8020
6010
012
014
0
14 12 10 8 6 4 2
Lib
rary
Fin
es
Book
s Bo
rrow
ed
Fines (dollars)
02
45
67
88
13
10
7 6 5 4 3 2 1
Cal
ori
es B
urn
edD
uri
ng
Exe
rcis
e
Tim
e (m
inut
es)
Calories
020
4010
3050
60
600
500
400
300
200
100
©G
lenc
oe/M
cGra
w-H
ill32
0G
lenc
oe A
lgeb
ra 1
Det
erm
ine
wh
eth
er e
ach
gra
ph
sh
ows
a po
siti
ve c
orre
lati
on,a
neg
ati
veco
rrel
ati
on,o
r n
o co
rrel
ati
on.I
f th
ere
is a
pos
itiv
e or
neg
ativ
e co
rrel
atio
n,
des
crib
e it
s m
ean
ing
in t
he
situ
atio
n.
1.2.
no c
orre
latio
nPo
sitiv
e;as
the
mea
n el
evat
ion
incr
ease
s,th
e hi
ghes
t po
int
incr
ease
s.D
ISEA
SEF
or E
xerc
ises
3–6
,use
th
e ta
ble
that
sh
ows
the
nu
mbe
r of
cas
es o
f m
um
ps
in t
he
Un
ited
Sta
tes
for
the
year
s 19
95 t
o 19
99.
3.D
raw
a s
catt
er p
lot
and
dete
rmin
e w
hat
rela
tion
ship
,if
any,
exis
ts in
the
dat
a.So
urce
:Cen
ters
for D
iseas
e Co
ntro
l and
Pre
vent
ion
Neg
ativ
e co
rrel
atio
n;as
the
yea
r
incr
ease
s,th
e nu
mbe
r of
cas
es d
ecre
ases
.4.
Dra
w a
line
of
fit
for
the
scat
ter
plot
.S
ampl
e an
swer
:Use
(19
96,7
51),
(199
7,68
3).
5.W
rite
the
slo
pe-i
nter
cept
for
m o
f an
equ
atio
n fo
r th
elin
e of
fit.
Sam
ple
answ
er:y
#!
68x
%13
6,47
96.
Pre
dict
the
num
ber
of c
ases
in 2
004.
abou
t 20
7
ZOO
SF
or E
xerc
ises
7–1
0,u
se t
he
tabl
e th
at
show
s th
e av
erag
e an
d m
axim
um
lon
gevi
ty o
fva
riou
s an
imal
s in
cap
tivi
ty.
7.D
raw
a s
catt
er p
lot
and
dete
rmin
e w
hat
rela
tion
ship
,if
any,
exis
ts in
the
dat
a.So
urce
: Wal
ker’s
Mam
mal
s of t
he W
orld
Pos
itive
cor
rela
tion;
as t
he a
vera
ge
incr
ease
s,th
e m
axim
um in
crea
ses.
8.D
raw
a li
ne o
f fi
t fo
r th
e sc
atte
r pl
ot.
Sam
ple
answ
er:U
se (
15,4
0),(
35,7
0).
9.W
rite
the
slo
pe-i
nter
cept
for
m o
f an
equ
atio
n fo
r th
e lin
e of
fit
.S
ampl
e an
swer
:y#
1.5x
%17
.510
.Pre
dict
the
max
imum
long
evit
y fo
r an
ani
mal
wit
h an
ave
rage
long
evit
y of
33
year
s.ab
out
67 y
r
An
imal
Lo
ng
evit
y (Y
ears
)
Ave
rage
Maximum
50
1015
2025
3035
4045
80 70 60 50 40 30 20 10
Long
evity
(ye
ars)
Avg
.12
2515
835
4041
20
Max
.47
5040
2070
7761
54
U.S
. Mu
mp
s C
ases
Year
Cases
1995
1997
1999
2001
1000 800
600
400
200 0
U.S
.Mum
ps C
ases
Year
1995
1996
1997
1998
1999
Cas
es90
675
168
366
638
7
Stat
e El
evat
ion
s
Mea
n El
evat
ion
(fee
t)
Highest Point(thousands of feet)
1000
020
0030
00
16 12 8 4
Sour
ce: U
.S. G
eolo
gical
Surv
ey
Tem
per
atu
re v
ersu
s R
ain
fall
Ave
rage
Ann
ual R
ainf
all (
inch
es)
AverageTemperature ($F)
1015
2025
3035
4045
64 60 56 52 0
Sour
ce: N
atio
nal O
cean
ic an
d At
mos
pher
ic Ad
min
istra
tion
Pra
ctic
e (A
vera
ge)
Sta
tistic
s:S
catt
er P
lots
and
Lin
es o
f Fit
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-7
5-7
Answers (Lesson 5-7)
© Glencoe/McGraw-Hill A22 Glencoe Algebra 1
Rea
din
g t
o L
earn
Math
emati
csS
tatis
tics:
Sca
tter
Plo
ts a
nd L
ines
of
Fit
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-7
5-7
©G
lenc
oe/M
cGra
w-H
ill32
1G
lenc
oe A
lgeb
ra 1
Lesson 5-7
Pre-
Act
ivit
yH
ow d
o sc
atte
r p
lots
hel
p i
den
tify
tre
nd
s in
dat
a?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 5-
7 at
the
top
of
page
298
in y
our
text
book
.
•W
hat
does
the
phr
ase
line
ar r
elat
ions
hip
mea
n to
you
?S
ampl
ean
swer
:It
mea
ns t
hat
whe
n yo
u gr
aph
the
data
poi
nts
on a
coor
dina
te g
rid,
the
poin
ts a
ll lie
on
or c
lose
to
a lin
e th
atyo
u co
uld
draw
on
the
grid
.
•W
rite
thr
ee o
rder
ed p
airs
tha
t fi
t th
e de
scri
ptio
n as
x i
ncre
ases
,yde
crea
ses.
Sam
ple
answ
er:{
(2,5
),(3
,3),
(4,1
)}
Read
ing
the
Less
on
1.L
ook
up t
he w
ord
scat
ter
in a
dic
tion
ary.
How
doe
s th
is d
efin
itio
n co
mpa
re t
o th
e te
rmsc
atte
r pl
ot?
One
def
initi
on s
tate
s “t
o oc
cur
or f
all i
rreg
ular
ly o
r at
rand
om.”
The
poin
ts in
a s
catt
er p
lots
usu
ally
do
not
follo
w a
n ex
act
linea
r pa
tter
n,bu
t fa
ll ir
regu
larl
y on
the
coo
rdin
ate
plan
e.
2.W
hat
is a
line
of
fit?
How
man
y da
ta p
oint
s fa
ll on
the
line
of
fit?
A li
ne o
f fit
sho
ws
the
tren
d of
the
dat
a.It
is im
poss
ible
to
say
how
man
y da
ta p
oint
s m
ayfa
ll on
a li
ne o
f fit
—m
aybe
sev
eral
,may
be n
one.
3.W
hat
is li
near
inte
rpol
atio
n? H
ow c
an y
ou d
isti
ngui
sh it
fro
m li
near
ext
rapo
lati
on?
Line
ar in
terp
olat
ion
is t
he p
roce
ss o
f pr
edic
ting
a y-
valu
e fo
r a
give
n x-
valu
e th
at li
es b
etw
een
the
leas
t an
d gr
eate
st x
-val
ues
in t
he d
ata
set.
“Int
er-”
mea
ns b
etw
een
and
“ext
ra-”
mea
ns b
eyon
d.If
the
x-va
lue
isbe
twee
n th
e ex
trem
es o
f th
e x-
valu
es in
the
dat
a se
t,yo
u sa
yin
terp
olat
ion;
if th
e x-
valu
e is
less
tha
n or
gre
ater
tha
n th
e ex
trem
es,
you
say
extr
apol
atio
n.
Hel
ping
You
Rem
embe
r
4.H
ow c
an y
ou r
emem
ber
whe
ther
a s
et o
f da
ta p
oint
s sh
ows
a po
siti
ve c
orre
lati
on o
r a
nega
tive
cor
rela
tion
?If
it lo
oks
like
a lin
e of
fit
for
the
poin
ts w
ould
hav
e a
posi
tive
slop
e,th
ere
is a
pos
itive
cor
rela
tion.
If it
look
s lik
e a
line
of f
itw
ould
hav
e a
nega
tive
slop
e,th
ere
is a
neg
ativ
e co
rrel
atio
n.
©G
lenc
oe/M
cGra
w-H
ill32
2G
lenc
oe A
lgeb
ra 1
Latit
ude
and
Tem
pera
ture
T
he l
atit
ude
of a
pla
ce o
n E
arth
is t
he m
easu
re o
f it
s di
stan
cefr
om t
he e
quat
or.W
hat
do y
outh
ink
is t
he r
elat
ions
hip
betw
een
a ci
ty’s
lati
tude
and
it
s Ja
nuar
y te
mpe
ratu
re?
At
the
righ
t is
a t
able
con
tain
ing
the
lati
tude
s an
d Ja
nuar
y m
ean
tem
pera
ture
s fo
r fi
ftee
nU
.S.c
itie
s.S
ampl
e an
swer
s ar
e gi
ven.
Sour
ces:
www.
indo
.com
and
www
.nws
.noa
a.gov
/clim
atex.h
tml
1.U
se t
he in
form
atio
n in
the
tab
le t
o cr
eate
a
scat
ter
plot
and
dra
w a
line
of
best
fit
fo
r th
e da
ta.
2.W
rite
an
equa
tion
for
the
line
of
fit.
Mak
e a
conj
ectu
re a
bout
the
rel
atio
nshi
p be
twee
n a
city
’s la
titu
de a
nd it
s m
ean
Janu
ary
tem
pera
ture
.y
!"
2.39
x#
121.
86;T
he h
ighe
rth
e la
titud
e,th
e lo
wer
the
tem
pera
ture
.
3.U
se y
our
equa
tion
to
pred
ict
the
Janu
ary
mea
n te
mpe
ratu
re o
f Ju
neau
,Ala
ska,
whi
ch h
as la
titu
de 5
8:23
N.
"17
.7$F
4.W
hat
wou
ld y
ou e
xpec
t to
be
the
lati
tude
of
a ci
ty w
ith
a Ja
nuar
y m
ean
tem
pera
ture
of
15°
F?
44:4
2 N
5.W
as y
our
conj
ectu
re a
bout
the
rel
atio
nshi
p be
twee
n la
titu
de a
nd t
empe
ratu
re c
orre
ct?
Yes;
as t
he la
titud
e in
crea
ses,
the
tem
pera
ture
dec
reas
es.
6.R
esea
rch
the
lati
tude
s an
d te
mpe
ratu
res
for
citi
es in
the
sou
ther
n he
mis
pher
e in
stea
d.D
oes
your
con
ject
ure
hold
for
the
se c
itie
s as
wel
l?Ye
s.
Lati
tude
($N
)
Temperature ($F)
70 60 50 40 30 20 10 0
!10T
L20
4060
1030
50
U.S
.City
Latit
ude
Janu
ary
Mea
n Te
mpe
ratu
re
Alb
any,
New
Yor
k42
:40
N20
.7°F
Alb
uque
rque
, New
Mex
ico
35:0
7 N
34.3
°F
Anc
hora
ge, A
lask
a61
:11
N14
.9°F
Birm
ingh
am, A
laba
ma
33:3
2 N
41.7
°F
Cha
rlest
on, S
outh
Car
olin
a32
:47
N47
.1°F
Chi
cago
, Illi
nois
41:5
0 N
21.0
°F
Col
umbu
s, O
hio
39:5
9 N
26.3
°F
Dul
uth,
Min
neso
ta46
:47
N7.
0°F
Fai
rban
ks, A
lask
a64
:50
N!
10.1
°F
Gal
vest
on, T
exas
29:1
4 N
52.9
°F
Hon
olul
u, H
awai
i21
:19
N72
.9°F
Las
Veg
as, N
evad
a36
:12
N45
.1°F
Mia
mi,
Flo
rida
25:4
7 N
67.3
°F
Ric
hmon
d, V
irgin
ia37
:32
N35
.8°F
Tucs
on, A
rizon
a32
:12
N51
.3°F
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
5-7
5-7
Answers (Lesson 5-7)
