1. Standard and Slope-Intercept Forms

2. Standard Form: Ax + By = C Slope-Intercept Form: y = mx + b IMPORTANT: B ≠ b You can convert between standard and slope-intercept forms by performing inverse operations. Inverse Operations: Multiply Divide Divide Multiply Add Subtract Subtract Add REMEMBER: Properties of Equality – what is done to one side of the equation must be done to the other side

3. How do you convert from standard form to slope-intercept form?
Ax + By = C y = mx + b
(Solve for y)
Example1: 6x + y = 12 (standard form)
(1)Subtract 6x from each side x x
y = -6x + 12 (slope-intercept form)
m = ______ b = ______
Example 2: x + 5y = 25 (standard form)
(1)Subtract 6x from each side x x
(2) Divide by 5 on each side y = -10x + 25
5 5
y = -2x + 5
TRY THESE: Convert from standard form to slope-intercept form
1. 40x – 5y = x + 2y = 30
3. x + y = x – y = 12

4. SOLUTIONS:
1. 40x – 5y = x + 2y = 30
3. x + y = x – y = 12
1) y = 8x + 2
y = 5x + 15
y = -x + (-7) or y = -x – 7
y = 2x – 12

5. How do you convert from slope-intercept form to standard form
How do you convert from slope-intercept form to standard form? y = mx + b Ax + By = C Example 1: y = 3x – 5 (slope-int form) (1) Subtract 3x from each side -3x -3x -3x + y = -5 (standard form) Example 2: y = 4 x + 12 (slope-int form) (1)Subtract 4 x from each side -4x -4x -4 x + y = 12 TRY THESE: Convert from slope-intercept form to standard form 1. y = 3 x – y = -x – 1 2. y = -10x – 2 4. y = x

6. SOLUTIONS:
1. y = 3 x – y = -x – 1
2. y = -10x – y = x
1) -3x + y = -15
10x + y = -2
x + y = -1
-x + y = 0