Algebra 1 · Unit 2
Rewrite a line as y = mx + b or as Ax + By = C.
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To y = mx + b
From standard form, move the x term, then divide by the coefficient of y. From point-slope form, distribute, then move the constant.
To Ax + By = C
Move the x term so x and y are on the same side. If a fraction is left, multiply by a common denominator.
A positive
If A is negative, multiply both sides by −1. A becomes positive, and every other sign flips.
Start with Ax + By = C.
2x − 4y = 12
−4y = −2x + 12
Divide by −4.
y = 12x − 3
Answer: y = 12x − 3
x + y = 9
y = −x + 9
Answer: y = −x + 9
3x + y = 12
y = −3x + 12
Answer: y = −3x + 12
−2x + y = 4
y = 2x + 4
Answer: y = 2x + 4
4x − 2y = 10
−2y = −4x + 10
Divide by −2.
y = 2x − 5
Answer: y = 2x − 5
2x + 4y = 8
4y = −2x + 8
Divide by 4.
y = −12x + 2
Answer: y = −12x + 2
Distribute, then solve for y.
y − 2 = 3(x − 1)
Distribute.
y − 2 = 3x − 3
Add 2 to both sides.
y = 3x − 1
Answer: y = 3x − 1
y − 4 = 2(x + 3)
Distribute.
y − 4 = 2x + 6
Add 4 to both sides.
y = 2x + 10
Answer: y = 2x + 10
y + 1 = −5(x − 2)
Distribute.
y + 1 = −5x + 10
Subtract 1 from both sides.
y = −5x + 9
Answer: y = −5x + 9
y − 6 = 12(x − 4)
Distribute.
y − 6 = 12x − 2
Add 6 to both sides.
y = 12x + 4
Answer: y = 12x + 4
y + 3 = −23(x − 6)
Distribute.
y + 3 = −23x + 4
Subtract 3 from both sides.
y = −23x + 1
Answer: y = −23x + 1
y − 8 = 4(x + 1)
Distribute.
y − 8 = 4x + 4
Add 8 to both sides.
y = 4x + 12
Answer: y = 4x + 12
Standard form of a line is Ax + By = C.
A is the number in front of x. B is the number in front of y. C is the number by itself.
Move the x term so x and y are on the same side. If a fraction is left, multiply by a common denominator.
Medium 4 stops when the fractions are gone. On that set, A can stay negative.
Move the x term. The slope is a negative integer.
y = −2x + 5
Add 2x to both sides.
2x + y = 5
Answer: 2x + y = 5
y = −3x + 1
Add 3x to both sides.
3x + y = 1
Answer: 3x + y = 1
y = −x + 8
Add x to both sides.
x + y = 8
Answer: x + y = 8
y = −5x − 2
Add 5x to both sides.
5x + y = −2
Answer: 5x + y = −2
y = −4x + 7
Add 4x to both sides.
4x + y = 7
Answer: 4x + y = 7
y = −6x
Add 6x to both sides.
6x + y = 0
Answer: 6x + y = 0
Move the x term, then multiply by the denominator.
y = −35x + 8
Add 35x to both sides.
35x + y = 8
Multiply by 5.
3x + 5y = 40
Answer: 3x + 5y = 40
y = −23x + 4
Add 23x to both sides.
23x + y = 4
Multiply by 3.
2x + 3y = 12
Answer: 2x + 3y = 12
y = −14x + 6
Add 14x to both sides.
14x + y = 6
Multiply by 4.
x + 4y = 24
Answer: x + 4y = 24
y = −32x + 5
Add 32x to both sides.
32x + y = 5
Multiply by 2.
3x + 2y = 10
Answer: 3x + 2y = 10
y = −45x − 1
Add 45x to both sides.
45x + y = −1
Multiply by 5.
4x + 5y = −5
Answer: 4x + 5y = −5
y = −16x + 3
Add 16x to both sides.
16x + y = 3
Multiply by 6.
x + 6y = 18
Answer: x + 6y = 18
Clear the fraction, then multiply by −1 if A is negative.
y = 23x + 7
Subtract 23x from both sides.
−23x + y = 7
Multiply by 3.
−2x + 3y = 21
A is negative. Multiply by −1.
2x − 3y = −21
Answer: 2x − 3y = −21
y = 12x + 5
Subtract 12x from both sides.
−12x + y = 5
Multiply by 2.
−x + 2y = 10
A is negative. Multiply by −1.
x − 2y = −10
Answer: x − 2y = −10
y = 34x − 2
Subtract 34x from both sides.
−34x + y = −2
Multiply by 4.
−3x + 4y = −8
A is negative. Multiply by −1.
3x − 4y = 8
Answer: 3x − 4y = 8
y = 25x + 1
Subtract 25x from both sides.
−25x + y = 1
Multiply by 5.
−2x + 5y = 5
A is negative. Multiply by −1.
2x − 5y = −5
Answer: 2x − 5y = −5
y = 13x + 4
Subtract 13x from both sides.
−13x + y = 4
Multiply by 3.
−x + 3y = 12
A is negative. Multiply by −1.
x − 3y = −12
Answer: x − 3y = −12
y = 52x + 3
Subtract 52x from both sides.
−52x + y = 3
Multiply by 2.
−5x + 2y = 6
A is negative. Multiply by −1.
5x − 2y = −6
Answer: 5x − 2y = −6
The slope and the y-intercept are both fractions. Multiply by a common denominator.
y = 14x + 23
Subtract 14x from both sides.
−14x + y = 23
Multiply by 12.
12 · (−14x) = −3x
12 · y = 12y
12 · (23) = 8
−3x + 12y = 8
Answer: −3x + 12y = 8
y = 12x + 13
Subtract 12x from both sides.
−12x + y = 13
Multiply by 6.
6 · (−12x) = −3x
6 · y = 6y
6 · (13) = 2
−3x + 6y = 2
Answer: −3x + 6y = 2
y = 23x + 12
Subtract 23x from both sides.
−23x + y = 12
Multiply by 6.
6 · (−23x) = −4x
6 · y = 6y
6 · (12) = 3
−4x + 6y = 3
Answer: −4x + 6y = 3
y = 15x + 34
Subtract 15x from both sides.
−15x + y = 34
Multiply by 20.
20 · (−15x) = −4x
20 · y = 20y
20 · (34) = 15
−4x + 20y = 15
Answer: −4x + 20y = 15
y = 34x − 16
Subtract 34x from both sides.
−34x + y = −16
Multiply by 12.
12 · (−34x) = −9x
12 · y = 12y
12 · (−16) = −2
−9x + 12y = −2
Answer: −9x + 12y = −2
y = 16x + 25
Subtract 16x from both sides.
−16x + y = 25
Multiply by 30.
30 · (−16x) = −5x
30 · y = 30y
30 · (25) = 12
−5x + 30y = 12
Answer: −5x + 30y = 12
Distribute, then write standard form with A positive and no fractions.
y − 3 = 2(x + 1)
Distribute.
y − 3 = 2x + 2
Add 3 to both sides.
y = 2x + 5
Subtract 2x from both sides.
−2x + y = 5
A is negative. Multiply by −1.
2x − y = −5
Answer: 2x − y = −5
y − 1 = 3(x − 2)
Distribute.
y − 1 = 3x − 6
Add 1 to both sides.
y = 3x − 5
Subtract 3x from both sides.
−3x + y = −5
A is negative. Multiply by −1.
3x − y = 5
Answer: 3x − y = 5
y + 2 = −4(x − 1)
Distribute.
y + 2 = −4x + 4
Subtract 2 from both sides.
y = −4x + 2
Add 4x to both sides.
4x + y = 2
Answer: 4x + y = 2
y − 5 = 12(x − 4)
Distribute.
y − 5 = 12x − 2
Add 5 to both sides.
y = 12x + 3
Subtract 12x from both sides.
−12x + y = 3
Multiply by 2.
−x + 2y = 6
A is negative. Multiply by −1.
x − 2y = −6
Answer: x − 2y = −6
y − 6 = −23(x + 3)
Distribute.
y − 6 = −23x − 2
Add 6 to both sides.
y = −23x + 4
Add 23x to both sides.
23x + y = 4
Multiply by 3.
2x + 3y = 12
Answer: 2x + 3y = 12
y + 1 = 5(x − 2)
Distribute.
y + 1 = 5x − 10
Subtract 1 from both sides.
y = 5x − 11
Subtract 5x from both sides.
−5x + y = −11
A is negative. Multiply by −1.
5x − y = 11
Answer: 5x − y = 11
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