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Standard and Slope-Intercept Forms

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Standard and Slope-Intercept Forms

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

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 -6x -6x

y = -6x + 12 (slope-intercept form)

m = ______ b = ______

Example 2: 10x + 5y = 25 (standard form)

(1)Subtract 6x from each side -10x -10x

(2) Divide by 5 on each side 5y = -10x + 25

55

y = -2x + 5

TRY THESE: Convert from standard form to slope-intercept form

1. 40x – 5y = -102. -10x + 2y = 30

3. x + y = -74. 2x – y = 12

SOLUTIONS:

1. 40x – 5y = -102. -10x + 2y = 30

3. x + y = -74. 2x – y = 12

1) y = 8x + 2

- y = 5x + 15
- y = -x + (-7) or y = -x – 7
- y = 2x – 12

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 – 153. y = -x – 1

2. y = -10x – 24. y = x

SOLUTIONS:

1. y = 3 x – 153. y = -x – 1

2. y = -10x – 24. y = x

1) -3x + y = -15

- 10x + y = -2
- x + y = -1
- -x + y = 0