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Amy Ferguson Moncure

Algebra 1 · Unit 2

Write Ax + By = C

Start with an equation in slope-intercept form. Rewrite it as Ax + By = C.

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Key Ideas Easy Medium Hard
What to Remember

Move the x term

Start from y = mx + b. Add or subtract the x term so x and y are on the same side.

Clear fractions

If a fraction is left, multiply both sides by the denominator. A, B, and C are integers.

A is a positive whole number

If A is negative, multiply both sides by −1. Every sign flips.

Easy

Integer slope

The slope is a negative integer. Move the x term.

Example
Write y = −7x + 4 in standard form.

y = −7x + 4

Add 7x to both sides.

7x + y = 4

Answer: 7x + y = 4

1
Write y = −8x + 3 in standard form.
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y = −8x + 3

Add 8x to both sides.

8x + y = 3

Answer: 8x + y = 3

2
Write y = −9x + 2 in standard form.
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y = −9x + 2

Add 9x to both sides.

9x + y = 2

Answer: 9x + y = 2

3
Write y = −x + 11 in standard form.
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y = −x + 11

Add x to both sides.

x + y = 11

Answer: x + y = 11

4
Write y = −4x − 9 in standard form.
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y = −4x − 9

Add 4x to both sides.

4x + y = −9

Answer: 4x + y = −9

5
Write y = −3x + 10 in standard form.
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y = −3x + 10

Add 3x to both sides.

3x + y = 10

Answer: 3x + y = 10

Medium

Fractional slope

The slope is a negative fraction. Move the x term, then multiply by the denominator.

Example
Write y = −25x + 7 in standard form.

y = −25x + 7

Add 25x to both sides.

25x + y = 7

Multiply by 5.

2x + 5y = 35

Answer: 2x + 5y = 35

1
Write y = −34x + 2 in standard form.
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y = −34x + 2

Add 34x to both sides.

34x + y = 2

Multiply by 4.

3x + 4y = 8

Answer: 3x + 4y = 8

2
Write y = −13x + 5 in standard form.
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y = −13x + 5

Add 13x to both sides.

13x + y = 5

Multiply by 3.

x + 3y = 15

Answer: x + 3y = 15

3
Write y = −52x − 3 in standard form.
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y = −52x − 3

Add 52x to both sides.

52x + y = −3

Multiply by 2.

5x + 2y = −6

Answer: 5x + 2y = −6

4
Write y = −27x + 1 in standard form.
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y = −27x + 1

Add 27x to both sides.

27x + y = 1

Multiply by 7.

2x + 7y = 7

Answer: 2x + 7y = 7

5
Write y = −43x + 6 in standard form.
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y = −43x + 6

Add 43x to both sides.

43x + y = 6

Multiply by 3.

4x + 3y = 18

Answer: 4x + 3y = 18

Hard

A must be positive

The slope is a positive fraction. Clear the fraction, then make A positive.

Example
Write y = 35x + 4 in standard form. A must be positive.

y = 35x + 4

Subtract 35x from both sides.

−35x + y = 4

Multiply by 5.

−3x + 5y = 20

A is negative. Multiply by −1.

3x − 5y = −20

Answer: 3x − 5y = −20

1
Write y = 14x + 6 in standard form. A must be positive.
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y = 14x + 6

Subtract 14x from both sides.

−14x + y = 6

Multiply by 4.

−x + 4y = 24

A is negative. Multiply by −1.

x − 4y = −24

Answer: x − 4y = −24

2
Write y = 32x − 1 in standard form. A must be positive.
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y = 32x − 1

Subtract 32x from both sides.

−32x + y = −1

Multiply by 2.

−3x + 2y = −2

A is negative. Multiply by −1.

3x − 2y = 2

Answer: 3x − 2y = 2

3
Write y = 27x + 3 in standard form. A must be positive.
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y = 27x + 3

Subtract 27x from both sides.

−27x + y = 3

Multiply by 7.

−2x + 7y = 21

A is negative. Multiply by −1.

2x − 7y = −21

Answer: 2x − 7y = −21

4
Write y = 43x + 5 in standard form. A must be positive.
Show Answer

y = 43x + 5

Subtract 43x from both sides.

−43x + y = 5

Multiply by 3.

−4x + 3y = 15

A is negative. Multiply by −1.

4x − 3y = −15

Answer: 4x − 3y = −15

5
Write y = 54x − 2 in standard form. A must be positive.
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y = 54x − 2

Subtract 54x from both sides.

−54x + y = −2

Multiply by 4.

−5x + 4y = −8

A is negative. Multiply by −1.

5x − 4y = 8

Answer: 5x − 4y = 8

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