# converting between standard form and slope-intercept form graphing unit

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Converting betweenConverting betweenStandard formStandard form

and and Slope-Intercept formSlope-Intercept form

Converting betweenConverting betweenStandard formStandard form

and and Slope-Intercept formSlope-Intercept form

Graphing UnitGraphing Unit

Slope-Intercept Formula

• This formula will be used to ___________and _____________ linear equations.

• To be able to use this formula, the equation you are graphing must be in this format!! This means to ______________________________________.

y mx b

write graph

Solve for “y ”

Slope-Intercept Formy = mx + b

• “x” and “y ” have to be on opposite sides of equation

• STEPS TO SOLVE FOR “Y”

• Add/Subtract the term that is on the same side of the equation with y

• Divide by the number in front

of y

Example 1 & 2 Write in slope-intercept form2 3 6x y 2x 2x

3y 2x 63 33

y 2

3x 2

6 9 3x y 6x 6x

9y 6x 39 9 9

y 2

3x

1

3

You tryit

Standard Form

• “x” and “y ” have to be on same side of equation

• “A” can’t be negative (AM sometimes breaks this rule)

• There can’t be any fractions

•

• STEPS • MULTIPLY BY LCD• MOVE “X” AND “Y”

TO SAME SIDE• MAKE SURE “X” IS

NOT NEGATIVE (Divide BY -1)

Ax + By = C

Example 3 Write in standard form

3 2

5 5y x (5) (5)

Multi

5y

Multiply

3xDivide

Multiply

23x3x

3x 5y 21 1 1

3 5 2x y

“x” and “Y” on

Same side

No negativesIn front

(5)

Divid

e

Example 4 Write in standard form

1 7

4 8y x (8) (8)

Multi

8y

Multiply

Divid

e

2xDivide

Multiply

72x2x

2x 8y 71 1 1

2 8 7x y

“x” and “Y” on

Same side

No negativesIn front

(8)

Example 5 Write in standard form

2 1

3 3y x (3) (3)

Multi

3y

Multiply

Divid

e

2xDivi

de

Multiply

12x2x

2x 3y 11 1 1

2 3 1x y

“x” and “Y” on

Same side

No negativesIn front

(3)

Example 6 Write in standard form

2 1

5 2y x

(10) (10)

Multi

10y

Multiply

Divide

4xDivi

de

Multiply

54x4x

4x 10y 5

“x” and “Y” on

Same side

(10)

Example 7 Write in standard form

12

3y x

(3) (3)

Multi

3y

Multiply

6xDivide

Multiply

16x6x

6x 3y 1

“x” and “Y” on

Same side

(3)

Example 8 Write in standard form

34

7y x (7) (7)

Multi

7y

Multiply

Divid

e

3x

Multiply

283x3x

3x 7y 281 1 1

3 7 28x y

“x” and “Y” on

Same side

No negativesIn front

(7)

Now let’s use the formula to WRITE an

equation.

y bmx

m = 3, b = 1

Write an equation in slope-intercept form when given the slope and the y-intercept.

Simply replace the “m” and the “b” in the formula with the numbers and you have an equation.

__ __y x 3 13 1y x

Write an equation in slope-intercept form when given the slope and the y-intercept.

m = -3, b = 5 m = ½ , b = 1

m = 0, b = 7 m = 4, b = -2

3 5y x 11

2y x

0 7y x 7y

4 2y x

Writing Slope-Intercept Equations - Examples