Math worksheet for practicing point-slope form equations of lines.

Let’s solve each problem one by one using the point-slope form of a line.

The point-slope formula is:

> y - y₁ = m(x - x₁)

Where:
- m is the slope
- (x₁, y₁) is the point the line passes through

We’ll plug in the values for each problem and simplify to get the equation in slope-intercept form (y = mx + b), unless otherwise specified. But since the worksheet just says “write each equation,” we can leave it in point-slope form or simplify — I’ll simplify to y = mx + b because that’s what most teachers expect.

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Problem 1:

m = 6 and (4, 12)

Plug into formula:
y - 12 = 6(x - 4)
→ y - 12 = 6x - 24
→ y = 6x - 24 + 12
→ y = 6x - 12

✔ Check: When x=4, y=6*4 -12 = 24-12=12 → correct.

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Problem 2:

m = 1/4 and (-3, -9)

y - (-9) = (1/4)(x - (-3))
→ y + 9 = (1/4)(x + 3)
→ y + 9 = (1/4)x + 3/4
→ y = (1/4)x + 3/4 - 9
→ y = (1/4)x + 3/4 - 36/4
→ y = (1/4)x - 33/4

✔ Check: Plug x=-3 → y=(1/4)(-3) -33/4 = -3/4 -33/4 = -36/4 = -9 → correct.

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Problem 3:

m = -7 and (-9, 5)

y - 5 = -7(x - (-9))
→ y - 5 = -7(x + 9)
→ y - 5 = -7x - 63
→ y = -7x - 63 + 5
→ y = -7x - 58

✔ Check: x=-9 → y=-7*(-9) -58 = 63 -58 = 5 → correct.

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Problem 4:

m = 1 and (6, -10)

y - (-10) = 1(x - 6)
→ y + 10 = x - 6
→ y = x - 6 - 10
→ y = x - 16

✔ Check: x=6 → y=6-16=-10 → correct.

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Problem 5:

m = -2 and (-1, -4)

y - (-4) = -2(x - (-1))
→ y + 4 = -2(x + 1)
→ y + 4 = -2x - 2
→ y = -2x - 2 - 4
→ y = -2x - 6

✔ Check: x=-1 → y=-2*(-1)-6=2-6=-4 → correct.

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Problem 6:

m = -3/5 and (2, -3)

y - (-3) = (-3/5)(x - 2)
→ y + 3 = (-3/5)(x - 2)
→ y + 3 = (-3/5)x + 6/5
→ y = (-3/5)x + 6/5 - 3
→ y = (-3/5)x + 6/5 - 15/5
→ y = (-3/5)x - 9/5

✔ Check: x=2 → y=(-3/5)*2 -9/5 = -6/5 -9/5 = -15/5 = -3 → correct.

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Problem 7:

m = -5/8 and (-8, -7)

y - (-7) = (-5/8)(x - (-8))
→ y + 7 = (-5/8)(x + 8)
→ y + 7 = (-5/8)x - 40/8
→ y + 7 = (-5/8)x - 5
→ y = (-5/8)x - 5 - 7
→ y = (-5/8)x - 12

✔ Check: x=-8 → y=(-5/8)*(-8) -12 = 5 -12 = -7 → correct.

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Problem 8:

m = 8 and (-5, 4)

y - 4 = 8(x - (-5))
→ y - 4 = 8(x + 5)
→ y - 4 = 8x + 40
→ y = 8x + 40 + 4
→ y = 8x + 44

✔ Check: x=-5 → y=8*(-5)+44 = -40+44=4 → correct.

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Problem 9:

Slope = 1/6, passing through (-9, 3)

y - 3 = (1/6)(x - (-9))
→ y - 3 = (1/6)(x + 9)
→ y - 3 = (1/6)x + 9/6
→ y - 3 = (1/6)x + 3/2
→ y = (1/6)x + 3/2 + 3
→ y = (1/6)x + 3/2 + 6/2
→ y = (1/6)x + 9/2

✔ Check: x=-9 → y=(1/6)*(-9) + 9/2 = -9/6 + 9/2 = -3/2 + 9/2 = 6/2 = 3 → correct.

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Final Answer:

1) y = 6x - 12
2) y = (1/4)x - 33/4
3) y = -7x - 58
4) y = x - 16
5) y = -2x - 6
6) y = (-3/5)x - 9/5
7) y = (-5/8)x - 12
8) y = 8x + 44
9) y = (1/6)x + 9/2