Math Worksheets For 8th Grade | 8th Grade Online Math Worksheets ... - Free Printable

Let's solve each problem step by step using the point-slope form of a line:

🔹 Point-Slope Form:

$$
y - y_1 = m(x - x_1)
$$
Where:
- $ m $ is the slope,
- $ (x_1, y_1) $ is a point on the line.

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Part 1: Given slope and a point

#### 1. $ m = 2 $ and $ (-1, -3) $
$$
y - (-3) = 2(x - (-1)) \Rightarrow y + 3 = 2(x + 1)
$$
✔ Answer: $ y + 3 = 2(x + 1) $

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#### 2. $ m = -7 $ and $ (1, -1) $
$$
y - (-1) = -7(x - 1) \Rightarrow y + 1 = -7(x - 1)
$$
✔ Answer: $ y + 1 = -7(x - 1) $

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#### 3. $ m = -2 $ and $ (-5, -2) $
$$
y - (-2) = -2(x - (-5)) \Rightarrow y + 2 = -2(x + 5)
$$
✔ Answer: $ y + 2 = -2(x + 5) $

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#### 4. $ m = 6 $ and $ (2, 5) $
$$
y - 5 = 6(x - 2)
$$
✔ Answer: $ y - 5 = 6(x - 2) $

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#### 5. $ m = 3 $ and $ (0, 10) $
$$
y - 10 = 3(x - 0) \Rightarrow y - 10 = 3x
$$
✔ Answer: $ y - 10 = 3x $

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#### 6. $ m = -9 $ and $ (8, 9) $
$$
y - 9 = -9(x - 8)
$$
✔ Answer: $ y - 9 = -9(x - 8) $

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#### 7. $ m = -1 $ and $ (-6, 12) $
$$
y - 12 = -1(x + 6)
$$
✔ Answer: $ y - 12 = -(x + 6) $

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#### 8. $ m = 0 $ and $ (3, 7) $
Zero slope means horizontal line.
$$
y - 7 = 0(x - 3) \Rightarrow y - 7 = 0
$$
✔ Answer: $ y - 7 = 0 $ (or simply $ y = 7 $, but in point-slope form: $ y - 7 = 0(x - 3) $)

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Part 2: Find equation through two points

We need to first find the slope $ m $, then use one point to write in point-slope form.

#### 9. $ (-1, 3) $ and $ (-2, 5) $

Step 1: Find slope:
$$
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 3}{-2 - (-1)} = \frac{2}{-1} = -2
$$

Now use one point, say $ (-1, 3) $:
$$
y - 3 = -2(x + 1)
$$
✔ Answer: $ y - 3 = -2(x + 1) $

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#### 10. $ (-7, 7) $ and $ (5, -6) $

Step 1: Find slope:
$$
m = \frac{-6 - 7}{5 - (-7)} = \frac{-13}{12}
$$

Use point $ (-7, 7) $:
$$
y - 7 = -\frac{13}{12}(x + 7)
$$
✔ Answer: $ y - 7 = -\frac{13}{12}(x + 7) $

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✔ Final Answers:

1. $ y + 3 = 2(x + 1) $
2. $ y + 1 = -7(x - 1) $
3. $ y + 2 = -2(x + 5) $
4. $ y - 5 = 6(x - 2) $
5. $ y - 10 = 3x $
6. $ y - 9 = -9(x - 8) $
7. $ y - 12 = -(x + 6) $
8. $ y - 7 = 0(x - 3) $
9. $ y - 3 = -2(x + 1) $
10. $ y - 7 = -\frac{13}{12}(x + 7) $

Let me know if you'd like these converted to slope-intercept form too!