Big IdeaEvery line has an equation of

the form Ax + By = C.

GoalWrite an equation for a line

in standard form.

1.Graph 5x + 2y = 10. 5x + 2y = 10 5(0) + 2y = 10 2y = 10 y = 5(0, 5)

5x + 2y = 10 5x + 2(0) = 10 5x = 10 x = 2(2, 0)

1 2 3 4 5

7

6

5

4

3

2

1

3. Rewrite y = −0.8x in standard from with integer values of A, B, & C.

2. Rewrite y = x - in

standard form with integer

coefficients. Tell the values of A, B, and C.

_ 3 1 5 5

_ 3 1 5 5

y = x-( )5

5y = -3x – 1+3x +3x

3x + 5y = -1

A = 3, B = 5, C = -1

y = -0.8x( )1010y = - 8x+8x +8x

8x + 10y = 0

Rewriting Equations in Slope-Intercept and Standard Form

Equation Slope-Intercept Form Standard Form

1. 20x - 5y = 352. y - 5 = 8(x - 1)3. 2x + 4(y + x) = 5y + 15

4. y = x + 11

5. 14x + 4y = 20

1. 20x - 5y = 35 20x – 5y = 35 4x – y = 7

( ) / 5

2. y – 5 = 8(x – 1) y – 5 = 8x – 8 y = 8x – 3

-8x -8x -8x + y = -3 -1( )

8x – y = 3

y = mx + b Ax + By = C

-1( ) y = 4x - 7

-4x -4x - y = -4x + 7

23

y = 4x – 7 4x – y = 7y = 8x – 3 8x – y = 3y = 6x – 15 6x - y = 15

y = x + 11 2x - 3y = -33

y = x + 5 7x + 2y = 10

23

_ 7 2

3. 2x + 4(y + x) = 5y + 15 4. y = x + 11 2x + 4y + 4x = 5y + 15 6x + 4y = 5y + 15 -5y -5y 6x - y = 15

-6x -6x - y = -6x + 15

5. 14x + 4y = 20

-1( ) y = 6x – 15

( ) / 2

y = x + 5

-1( ) 2x - 3y = -33

23

y = x + 1123

3( )

3y = 2x + 33 -2x -2x-2x + 3y = 33

( ) / 2 7x + 2y = 10

-7x -7x 2y = -7x + 10

_ 7 2

Lourdes spent $24 on 30 neon bouncing balls and 12glow-in-the-dark necklaces. Write an equation in standard formthen answer the questions below.

1. If a neon ball cost $0.30, then how much did a necklace cost?2. What is the most a necklace could have cost? What is the cost of one neon ball?3. What is the most a neon ball could have cost?

#neon balls price of 1 ball + #necklaces price of 1 necklace = total

30x + 12y = 24

1. 30x + 12y = 24 30(.30) + 12y = 24 9 + 12y = 24 12y = 15 y = 1.25 a necklace costs $1.25

2. Max when 0 neon balls 30(0) + 12y = 24 12y = 24 y = 2Max price of a necklace $2.00Neon ball is free.

3. Max when 0 necklaces 30x + 12(0) = 24 30x = 24 x = .8Max price of a neon ball $.80