Let’s solve each problem step by step. We’ll use the point-slope form:
y - y₁ = m(x - x₁)
Then we’ll solve for
y to get it in slope-intercept form (y = mx + b).
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Problem 1: Slope = -4, Point = (-1, -3)
Start with point-slope:
y - (-3) = -4(x - (-1))
→ y + 3 = -4(x + 1)
Distribute:
y + 3 = -4x - 4
Subtract 3 from both sides:
y = -4x - 7
✔ Final Answer for #1:
y = -4x - 7
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Problem 2: Slope = -1/9, Point = (-9, 6)
Point-slope:
y - 6 = (-1/9)(x - (-9))
→ y - 6 = (-1/9)(x + 9)
Distribute:
y - 6 = (-1/9)x - 1
Add 6 to both sides:
y = (-1/9)x + 5
✔ Final Answer for #2:
y = -\frac{1}{9}x + 5
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Problem 3: Slope = 3, Point = (1, -1)
Point-slope:
y - (-1) = 3(x - 1)
→ y + 1 = 3x - 3
Subtract 1:
y = 3x - 4
✔ Final Answer for #3:
y = 3x - 4
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Problem 4: Slope = -11/4, Point = (4, -4)
Point-slope:
y - (-4) = (-11/4)(x - 4)
→ y + 4 = (-11/4)(x - 4)
Distribute:
y + 4 = (-11/4)x + 11 [because (-11/4)*(-4) = +11]
Subtract 4:
y = (-11/4)x + 7
✔ Final Answer for #4:
y = -\frac{11}{4}x + 7
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Problem 5: Slope = undefined, Point = (-4, -8)
Undefined slope means a
vertical line.
Vertical lines have equations like
x = constant.
Since it passes through x = -4, the equation is:
x = -4
But note: you cannot write this as “solve for y” — because y can be anything. So we leave it as x = -4.
✔ Final Answer for #5:
x = -4
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Problem 6: Slope = 10/9, Point = (-9, -9)
Point-slope:
y - (-9) = (10/9)(x - (-9))
→ y + 9 = (10/9)(x + 9)
Distribute:
y + 9 = (10/9)x + 10 [because (10/9)*9 = 10]
Subtract 9:
y = (10/9)x + 1
✔ Final Answer for #6:
y = \frac{10}{9}x + 1
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Problem 7: Slope = 4/7, Point = (7, -3)
Point-slope:
y - (-3) = (4/7)(x - 7)
→ y + 3 = (4/7)(x - 7)
Distribute:
y + 3 = (4/7)x - 4 [because (4/7)*7 = 4]
Subtract 3:
y = (4/7)x - 7
✔ Final Answer for #7:
y = \frac{4}{7}x - 7
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Problem 8: Slope = 3/4, Point = (-4, 6)
Point-slope:
y - 6 = (3/4)(x - (-4))
→ y - 6 = (3/4)(x + 4)
Distribute:
y - 6 = (3/4)x + 3 [because (3/4)*4 = 3]
Add 6:
y = (3/4)x + 9
✔ Final Answer for #8:
y = \frac{3}{4}x + 9
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Problem 9: Slope = -4/3, Point = (-9, 5)
Point-slope:
y - 5 = (-4/3)(x - (-9))
→ y - 5 = (-4/3)(x + 9)
Distribute:
y - 5 = (-4/3)x - 12 [because (-4/3)*9 = -12]
Add 5:
y = (-4/3)x - 7
✔ Final Answer for #9:
y = -\frac{4}{3}x - 7
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Problem 10: Slope = -13/4, Point = (4, -8)
Point-slope:
y - (-8) = (-13/4)(x - 4)
→ y + 8 = (-13/4)(x - 4)
Distribute:
y + 8 = (-13/4)x + 13 [because (-13/4)*(-4) = +13]
Subtract 8:
y = (-13/4)x + 5
✔ Final Answer for #10:
y = -\frac{13}{4}x + 5
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Final Answer:
1. y = -4x - 7
2. y = -\frac{1}{9}x + 5
3. y = 3x - 4
4. y = -\frac{11}{4}x + 7
5. x = -4
6. y = \frac{10}{9}x + 1
7. y = \frac{4}{7}x - 7
8. y = \frac{3}{4}x + 9
9. y = -\frac{4}{3}x - 7
10. y = -\frac{13}{4}x + 5
Parent Tip: Review the logic above to help your child master the concept of finding slope from 2 points worksheet.
