Geometry Interactive Notebook 3-6

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' P l 0 . . N \ L

P o i n t - S lo p e F o r m

H o r i z o n t a l

l i n e

S i o p e - I n t e r t e p t

F o r m

V e r t i t a l

l i n e



Given the slope, m, and a point on the line ( X1'Y1)'

the equation of the line i6

y - y 1 ; ;: ;; ::m ( x - x , )

Example: Write the equa tlon of the line whose

slope is 2, which goes through the point

(1,6)

y-6 =2(x-1)

For a horizontal line (m =0), the equation of the

line is

y=b

Given the slope, rn , and , the y-intercept, the

equation of the line is

y = tx + b

Example: For m =-3and y-intercept 7, find t

equation of the line.

y =-3x+7

For a vertical line (m = undefined), the equatio

the line is

X = x1

Notice that this equation does not start with " s= "



WtL+-e . . . ~j!. e ' 1 Y ( ' t . , 1 : m \ l \ S . . \'I\_ 5 . \Q Pe . -1V ' \ i~1" '( . .~p+ ~rrnI I

5._ Y Y \ . = 1:."i b : : . {p_ _ _~,-rn::_];_1 b ' : ! 3 .

~~ i.x + - ~ y ~ ~ X + 3 -



Step 1: Plot the givenpoint

Step 2: From this point, count

the "rise" up if the slope is

positive and down jf the

slope is negative

Step 3: From this new location,

Gaunt the "run" to the

right..

Step 4: Mark this point and

connect the two points.



Step 1: Plot the given point

Step 2: From this point, count

the "rise" t i l ? if the slope is

positive and down if the

slope is negative

Step 3: From this new location,count the "run" to the

right.

Step 4: Mark this point and

connect the two points.

y

Weare givet:1he y-intercept, so weput a point at

(0,3)

2Our slope is --, so our rise will be-2.

3

The run of our slope will be3.

y



x

. x

x

3. ~ = ( j 1 ' {g)y

x

y

i



Two~ \\i\~ w . l n d D 1)(\e_ c J r ~r-ee_ - ± \ A H ( ) ~ ~ _ ' "

• N o + 1Y\- le ,c~eQ_1- (pcvraJle . l )

l l ' : r ~ £ £ s , ~ + e t + o Y ' l -e . . .c p n \ C 1 + :

~ \ l\_ tu .: ~e.c. . t- ( ? t ' L n p0\Y\-:\:~ (~O". "!!d~)

lO_dct-et":wHrtL J.uln\ctn of ~~e . . . po$ibtlrhe.s lS to.)', _

l c o k o J : + h e . - - s t o p e . . s o ..;yJ ~ ~ 'h , : ·h!~r£ .e . .p+~h

Coinciding Line€)arallel Lines Intersecting

Lines

same slope,

same intercept

-- same slope.

different

intercept

different slopes

- ..To eJ)mflU~ s\opf!:) C V l 1 d ~- tn t -u :~~~) put ~ __

- +t _~vo .b rn s \ ' C \ ~ \op f . . , - u , \ 1 : o c c , t , f l t ~ rN \ Cy~ f f iX-+ b ) . _

.A ~ dOl~ ~ +0 ~,<l- J t L S t e ~ u t L - h o V \ ! WL tllA t\.. _

'f.L w h ¥ ~~< -two. tlf\~ c O \ V ' \ C A d _ e . J _

1--: : - 3(X-t )

\ 1 - f & _ '= ? : , X - . 3+ -5 + 6

~ ~ -:1.+1-



" P r G t C - h c . . . e . .

\ J . e . v \ - h ~ w k ~ " " " e . ¥ ~ e, \U'\.t.s IV\~-~~&t CDI(\ C - I d f_ )

. OC Me, ~ o J \ e . 1 L

L \ f , : ;~+3 L L: f \ - rU 'S-c.c . .Tt ' 0y- :~ - f t J _

2.. i""~)(> ~(l.\ \ e . . \\f~tJxE])

3, ~~®'6>~h(. .2 . ~ = - \ 2 . . p o . K " O - . t \ i e . . \

-?.~-= -4 x +ll-

' 1 ~ C 9

\ . \ . ~ - 2y ':- \1 ..1

-2 ~ = = . . ) ( - \~

~:;\ i~tj)

~ . . b f ~ t(x +-~ ' )

' y - q = = iX-l-3

Y ~'J,}fj)

Geometry Interactive Notebook 3-6

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