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Amy Ferguson Moncure

Algebra 1 · Unit 2

Write y = mx + b

Write a line in slope-intercept form from a slope and intercept, a slope and a point, or two points.

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Key Ideas Easy Medium Hard
What to Remember

Slope and y-intercept

If you know m and b, write y = mx + b.

Slope and a point

Substitute the point into y = mx + b and solve for b.

Two points

Find the slope first. m = y₂ − y₁x₂ − x₁. Then substitute one point to find b.

Easy

Slope and y-intercept

The slope and the y-intercept are given.

Example
Write the equation of the line with slope 2 and y-intercept (0, 5).

y = mx + b

m = 2

b = 5

y = 2x + 5

Answer: y = 2x + 5

1
Write the equation of the line with slope −3 and y-intercept (0, 4).
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y = mx + b

m = −3

b = 4

y = −3x + 4

Answer: y = −3x + 4

2
Write the equation of the line with slope 12 and y-intercept (0, −1).
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y = mx + b

m = 12

b = −1

y = 12x − 1

Answer: y = 12x − 1

3
Write the equation of the line with slope 0 and y-intercept (0, 6).
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y = mx + b

m = 0

b = 6

y = 6

Answer: y = 6

4
Write the equation of the line with slope 4 and y-intercept (0, 0).
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y = mx + b

m = 4

b = 0

y = 4x

Answer: y = 4x

5
Write the equation of the line with slope −23 and y-intercept (0, 7).
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y = mx + b

m = −23

b = 7

y = −23x + 7

Answer: y = −23x + 7

Medium

Slope and a point

The point is not the y-intercept. Solve for b.

Example
Write y = mx + b for the line with slope 3 through (2, 11).

The slope is 3.

Substitute (2, 11).

y = mx + b

11 = 3(2) + b

11 = 6 + b

11 − 6 = b

b = 5

y = 3x + 5

Answer: y = 3x + 5

1
Write y = mx + b for the line with slope 2 through (4, 3).
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The slope is 2.

Substitute (4, 3).

y = mx + b

3 = 2(4) + b

3 = 8 + b

3 − 8 = b

b = −5

y = 2x − 5

Answer: y = 2x − 5

2
Write y = mx + b for the line with slope −1 through (5, 2).
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The slope is −1.

Substitute (5, 2).

y = mx + b

2 = −(5) + b

2 = −5 + b

2 + 5 = b

b = 7

y = −x + 7

Answer: y = −x + 7

3
Write y = mx + b for the line with slope 12 through (6, 5).
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The slope is 12.

Substitute (6, 5).

y = mx + b

5 = 12(6) + b

5 = 3 + b

5 − 3 = b

b = 2

y = 12x + 2

Answer: y = 12x + 2

4
Write y = mx + b for the line with slope −4 through (−1, 6).
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The slope is −4.

Substitute (−1, 6).

y = mx + b

6 = −4(−1) + b

6 = 4 + b

6 − 4 = b

b = 2

y = −4x + 2

Answer: y = −4x + 2

5
Write y = mx + b for the line with slope 34 through (8, 1).
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The slope is 34.

Substitute (8, 1).

y = mx + b

1 = 34(8) + b

1 = 6 + b

1 − 6 = b

b = −5

y = 34x − 5

Answer: y = 34x − 5

Hard

Two points

Find the slope, then find b.

Example
Write y = mx + b for the line through (1, 4) and (3, 10).

m = y₂ − y₁x₂ − x₁

m = 62

m = 3

Use (1, 4).

y = mx + b

4 = 3(1) + b

4 = 3 + b

4 − 3 = b

b = 1

y = 3x + 1

Answer: y = 3x + 1

1
Write y = mx + b for the line through (2, 1) and (6, 9).
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m = y₂ − y₁x₂ − x₁

m = 84

m = 2

Use (2, 1).

y = mx + b

1 = 2(2) + b

1 = 4 + b

1 − 4 = b

b = −3

y = 2x − 3

Answer: y = 2x − 3

2
Write y = mx + b for the line through (−2, 5) and (2, −3).
Show Answer

m = y₂ − y₁x₂ − x₁

m = −84

m = −2

Use (−2, 5).

y = mx + b

5 = −2(−2) + b

5 = 4 + b

5 − 4 = b

b = 1

y = −2x + 1

Answer: y = −2x + 1

3
Write y = mx + b for the line through (1, 6) and (4, 6).
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m = y₂ − y₁x₂ − x₁

m = 03

m = 0

Use (1, 6).

y = mx + b

6 = −0(1) + b

6 = 0 + b

6 − 0 = b

b = 6

y = 6

Answer: y = 6

4
Write y = mx + b for the line through (3, −1) and (6, 5).
Show Answer

m = y₂ − y₁x₂ − x₁

m = 63

m = 2

Use (3, −1).

y = mx + b

−1 = 2(3) + b

−1 = 6 + b

−1 − 6 = b

b = −7

y = 2x − 7

Answer: y = 2x − 7

5
Write y = mx + b for the line through (2, 3) and (6, 5).
Show Answer

m = y₂ − y₁x₂ − x₁

m = 24

m = 12

Use (2, 3).

y = mx + b

3 = 12(2) + b

3 = 1 + b

3 − 1 = b

b = 2

y = 12x + 2

Answer: y = 12x + 2

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