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

STANDARD FORM OF A LINEAR EQUATION

Day 1

SECTION 5.5a

Page 2: 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

Page 3: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

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

Page 4: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

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 !!!

Page 5: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

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

Page 6: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

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

Page 7: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

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

Page 8: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

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

Page 9: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

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

Page 10: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

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

Page 11: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

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

Page 12: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

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

Page 13: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

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

B.

x- intercept y-intercept

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

Page 14: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

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

C.

x- intercept y-intercept

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

Page 15: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

x- intercept y-intercept

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

Page 16: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

Ax By C Ax

By Ax C B B B

A C

y xB B

x- intercept y-intercept

C

xA

intercept ,0C

xA

C

yB

intercept 0,C

yB

Ax By C

A

mB

Page 17: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

x - intercept =

y - intercept = Slope =

Ax CBy

B

A

Page 18: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

x - intercept =

y - intercept = Slope =

C

A

Ax CBy

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

B

A

Page 19: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

x - intercept =

y - intercept = Slope =

C

A

Ax CBy

B

A

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

C

B

Page 20: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

-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

Page 21: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

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

A. -3 2 12x y A =

B =

C =

3

2

12Slope x- intercept y-intercept

Am

B

- int

Cx

A

3

2m

3

2m

3- int

12x

- int 4x

Page 22: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

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

A. -3 2 12x y A =

B =

C =

3

2

12Slope x- intercept y-intercept

Am

B

- int

Cx

A -int

Cy

B

3

2m

3

2m

3- int

12x

- int 4x

- int12

2y

- int 6y

Page 23: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

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

A. -3 2 12x y A =

B =

C =

3

2

12Slope x- intercept y-intercept

Am

B

- int

Cx

A -int

Cy

B

3

2m

3

2m

3- int

12x

- int 4x

- int12

2y

- int 6y

Page 24: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

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

B.

A =

B =

C =

5

3

30Slope x- intercept y-intercept

Am

B

5

3m

5

3m

5 3 30x y

Page 25: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

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

B.

A =

B =

C =

5

3

30Slope x- intercept y-intercept

Am

B

5

3m

5

3m

5 3 30x y

- intC

xA

- int30

5x

- int 6x

Page 26: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

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

B.

A =

B =

C =

5

3

30Slope x- intercept y-intercept

Am

B

5

3m

5

3m

5 3 30x y

- intC

xA

- int30

5x

- int 6x

-intC

yB

3- int

30y

- int 10y

Page 27: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

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

B.

A =

B =

C =

5

3

30Slope x- intercept y-intercept

Am

B

5

3m

5

3m

5 3 30x y

- intC

xA

- int30

5x

- int 6x

-intC

yB

3- int

30y

- int 10y

Page 28: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

4 6 12x y

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

C.

A =

B =

C =

4

6

12Slope x- intercept y-intercept

Am

B

4

6m

2

3m

Page 29: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

4 6 12x y

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

C.

A =

B =

C =

4

6

12Slope x- intercept y-intercept

Am

B

4

6m

2

3m

- intC

xA

2- int

1

4x

- int 3x

Page 30: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

4 6 12x y

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

C.

A =

B =

C =

4

6

12Slope x- intercept y-intercept

Am

B

4

6m

2

3m

- intC

xA

2- int

1

4x

- int 3x

-intC

yB

2- int

1

6y

- int 2y

Page 31: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

4 6 12x y

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

C.

A =

B =

C =

4

6

12Slope x- intercept y-intercept

Am

B

4

6m

2

3m

- intC

xA

2- int

1

4x

- int 3x

-intC

yB

2- int

1

6y

- int 2y

Page 32: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

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

Ax By C

x & y intercepts

Page 33: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

Example 6: Graph the following equations.

-3 2 12x y

A.

- intC

xA

124

3

Page 34: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

Example 6: Graph the following equations.

-3 2 12x y

A.

- intC

xA

124

3

-intC

yB

612

2

Page 35: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

Example 6: Graph the following equations.

-3 2 12x y

A.

- intC

xA

124

3

-intC

yB

612

2

Page 36: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

4 8x y

Example 6: Graph the following equations.

B.

- intC

xA

8

42

Page 37: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

4 8x y

Example 6: Graph the following equations.

B.

- intC

xA

8

42

-intC

yB

8

18

Page 38: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

4 8x y

Example 6: Graph the following equations.

B.

- intC

xA

8

42

-intC

yB

8

18

Page 39: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

4 6 12x y

Example 6: Graph the following equations.

C.

- intC

xA

312

4

Page 40: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

4 6 12x y

Example 6: Graph the following equations.

C.

- intC

xA

312

4

-intC

yB

6

212

Page 41: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

4 6 12x y

Example 6: Graph the following equations.

C.

- intC

xA

312

4

-intC

yB

6

212

Page 42: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

6 5 30x y

Example 6: Graph the following equations.

D.

- intC

xA

30

65

Page 43: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

6 5 30x y

Example 6: Graph the following equations.

D.

- intC

xA

30

65

-intC

yB

30

56

Page 44: STANDARD FORM OF A LINEAR EQUATION Day 1 SECTION 5.5a.

6 5 30x y

Example 6: Graph the following equations.

D.

- intC

xA

30

65

-intC

yB

30

56