STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

STANDARD FORM OF A LINEAR EQUATION

Day 1

SECTION 5.5a

The equation 2 3y x is written _______________ form.

If we move “ 2xwe have _______________________.

” to the other side of the equation,

2 3y x slope intercept

2x

2 3x y

2 3x y

If we move “ 2xwe have _______________________.

” to the other side of the equation,

2 3x y

This is still a ________ equation, but it is written in a different form.

linear

A linear equation in the form _______________ is in ______________, where A, B, and C are integers.

Ax By C standard form

A linear equation in the form _______________ is in ______________, where A, B, and C are integers.

Ax By C standard form

Remember the set of integers is

.... 4, 3, 2, 1, 0,1, 2, 3, 4...

NO FRACTIONS!!!NO DECIMALS !!!

Example 1:A. Jackie is in charge of selling tickets for the school jazz

concert at $2.00 for students and $4.00 for adults. She hopes that the total ticket sales will be about $600 in order to cover expenses and make a modest profit. Write a linear equation in standard form to model this

situation.

Let x y

# student tickets

# adult tickets

$2.00

$4.00

2.00 4.00 600x y

2 4 600x y

B. A donation of $300 was make to the Classical Music Club for the purpose of building their collection of CDs. At the local music store, some classical CDs cost $10 and other cost $15. The club wants to know how many of each type can buy with the $300.

(Do not consider sales tax.) Write an equation in standard form to model this

situation.Let x

y

# classical CDs

# other CDs

$10.00

$15.00

10.00 15.00 300x y

10 15 300x y

5 2 4y x

x-term + y-term = constantNo fractions, no decimals ! 4 2 2x y

5 8

7y x

2 5

3x y

7 3 5x y

7.5 4.3x y

A

B

C

D

E

F

Example 2: Tell whether the equations below are in standard form.

NO

YES

NO

NO

YES

NO

FRACTIONS

DECIMALS

If an equation is not written in standard form, we can rewrite the equation so that it is in standard form.

Example 3: Write each linear equation in standard form.

A. 57 2 4y x B. 3 8

7y x 2y

57 4 2x y

4 2 57x y

7 7 7

7 3 56y x 3x

3 7 56x y

3 7 56x y 4 2 57x y

C. 57 2 4y x D.

53

57 40 53x y

57 4 2x y

2y

4 2 57x y

4 2 57x y 57 40 53x y

5.7 5.3 4x y 10 10 10

57 53 40x y 40y

We can find the ___& ___ intercepts and the ________ when the equation is written in standard form.

x y slope

x-intercept is at

y

y-intercept is at

x ( 2,0)

0

(0,3)

0

x-intercept is at

y

y-intercept is at

x ( 2,0)

0

(0,3)

0

We know that y = 0 at the ____ intercept, so we can plug in 0 for ___ to find the _____ intercept.

We know that x = 0 at the ____ intercept, so we can plug in 0 for ___ to find the _____ intercept.

xy x

yyx

Example 4: Find the x & y intercepts of the following equations.

A. 4 2 12x y

x- intercept y-intercept

Plug in 0 for y

Plug in 0 for x

0 4 2 12x

4 12x 4 4

3x

intercept 3,0x

4 10 2 2y

2 12y 2 2

6y

intercept 0, 6y


B.


Plug in 0 for y

Plug in 0 for x

2 3 180x

2 18x 2 2

9x

intercept 9,0x

2 3 10 8y

3 18y 3 3

6y

intercept 0, 6y

2 3 18x y


C.


Plug in 0 for y

Plug in 0 for x

0 Ax B C

Ax C A A

C

xA

intercept ,0C

xA

0A By C By C

B B

C

yB

intercept 0,C

yB

Ax By C


C

xA

intercept ,0C

xA

C

yB

intercept 0,C

yB

Ax By C

Write in slope-intercept form to find the slope. Ax By C

Ax By C Ax

By Ax C B B B

A C

y xB B


C

xA

intercept ,0C

xA

C

yB

intercept 0,C

yB

Ax By C

A

mB

x - intercept =

y - intercept = Slope =

Ax CBy

B

A

x - intercept =


C

A

Ax CBy

To find the x-intercept, cross out the y-term…

B

A

x - intercept =


C

A

Ax CBy

B

A

To find the y-intercept, cross out the x-term…

C

B

-3 2 12x y

Example 5: Find the slope and x & y intercepts of the following equations.

A.

A =

B =

C =

3

2

12Slope x- intercept y-intercept

Am

B

3

2m

3

2m


A. -3 2 12x y A =

B =

C =

3

2


Am

B

- int

Cx

A

3

2m

3

2m

3- int

12x

- int 4x


A. -3 2 12x y A =

B =

C =

3

2


Am

B

- int

Cx

A -int

Cy

B

3

2m

3

2m

3- int

12x

- int 4x

- int12

2y

- int 6y


B.

A =

B =

C =

5

3


Am

B

5

3m

5

3m

5 3 30x y


B.

A =

B =

C =

5

3


Am

B

5

3m

5

3m

5 3 30x y

- intC

xA

- int30

5x

- int 6x


B.

A =

B =

C =

5

3


Am

B

5

3m

5

3m

5 3 30x y

- intC

xA

- int30

5x

- int 6x

-intC

yB

3- int

30y

- int 10y

4 6 12x y


C.

A =

B =

C =

4

6


Am

B

4

6m

2

3m

4 6 12x y


C.

A =

B =

C =

4

6


Am

B

4

6m

2

3m

- intC

xA

2- int

1

4x

- int 3x

4 6 12x y


C.

A =

B =

C =

4

6


Am

B

4

6m

2

3m

- intC

xA

2- int

1

4x

- int 3x

-intC

yB

2- int

1

6y

- int 2y

If an equation is written in standard form, you can use the _______________ to graph the equation quickly.

Ax By C

x & y intercepts

Example 6: Graph the following equations.

-3 2 12x y

A.

- intC

xA

124

3


-3 2 12x y

A.

- intC

xA

124

3

-intC

yB

612

2

4 8x y


B.

- intC

xA

8

42

4 8x y


B.

- intC

xA

8

42

-intC

yB

8

18

4 6 12x y


C.

- intC

xA

312

4

4 6 12x y


C.

- intC

xA

312

4

-intC

yB

6

212

6 5 30x y


D.

- intC

xA

30

65

6 5 30x y


D.

- intC

xA

30

65

-intC

yB

30

56

STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

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