Parallel Lines Worksheets featuring six problems to find equations of parallel lines in slope-intercept form.

Let's solve each problem step by step. We are asked to find the equation of a line parallel to a given line and passing through a given point, and write the answer in slope-intercept form:
$$
y = mx + b
$$

🔍 Key Concept:

- Parallel lines have the same slope.
- So, we take the slope from the given line and use it with the point-slope form to find the new equation.

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✔ Problem 1:

Given: $ y = -4x + 4 $ and point $ (-4, 3) $

- Slope $ m = -4 $
- Use point-slope form: $ y - y_1 = m(x - x_1) $
- Plug in: $ y - 3 = -4(x + 4) $
- Simplify:
$$
y - 3 = -4x - 16 \\
y = -4x - 13
$$

✔ Answer: $ \boxed{y = -4x - 13} $

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✔ Problem 2:

Given: $ y = -\frac{4}{3}x + 1 $ and point $ (0, 5) $

- Slope $ m = -\frac{4}{3} $
- Point is $ (0, 5) $ — this is the y-intercept!
- So, directly: $ y = -\frac{4}{3}x + 5 $

✔ Answer: $ \boxed{y = -\frac{4}{3}x + 5} $

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✔ Problem 3:

Given: $ y = -\frac{2}{5}x - 2 $ and point $ (-5, -3) $

- Slope $ m = -\frac{2}{5} $
- Use point-slope: $ y + 3 = -\frac{2}{5}(x + 5) $
- Simplify:
$$
y + 3 = -\frac{2}{5}x - 2 \\
y = -\frac{2}{5}x - 5
$$

✔ Answer: $ \boxed{y = -\frac{2}{5}x - 5} $

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✔ Problem 4:

Given: $ y = \frac{5}{2}x - 4 $ and point $ (3, -1) $

- Slope $ m = \frac{5}{2} $
- Use point-slope: $ y + 1 = \frac{5}{2}(x - 3) $
- Simplify:
$$
y + 1 = \frac{5}{2}x - \frac{15}{2} \\
y = \frac{5}{2}x - \frac{15}{2} - 1 = \frac{5}{2}x - \frac{17}{2}
$$

✔ Answer: $ \boxed{y = \frac{5}{2}x - \frac{17}{2}} $

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✔ Problem 5:

Given: $ y = -\frac{2}{3}x - 2 $ and point $ (-2, -3) $

- Slope $ m = -\frac{2}{3} $
- Use point-slope: $ y + 3 = -\frac{2}{3}(x + 2) $
- Simplify:
$$
y + 3 = -\frac{2}{3}x - \frac{4}{3} \\
y = -\frac{2}{3}x - \frac{4}{3} - 3 = -\frac{2}{3}x - \frac{13}{3}
$$

✔ Answer: $ \boxed{y = -\frac{2}{3}x - \frac{13}{3}} $

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✔ Problem 6:

Given: $ y = -x + 4 $ and point $ (-1, 4) $

- Slope $ m = -1 $
- Use point-slope: $ y - 4 = -1(x + 1) $
- Simplify:
$$
y - 4 = -x - 1 \\
y = -x + 3
$$

✔ Answer: $ \boxed{y = -x + 3} $

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📌 Final Answers Summary:

| Problem | Equation |
|--------|---------|
| 1 | $ y = -4x - 13 $ |
| 2 | $ y = -\frac{4}{3}x + 5 $ |
| 3 | $ y = -\frac{2}{5}x - 5 $ |
| 4 | $ y = \frac{5}{2}x - \frac{17}{2} $ |
| 5 | $ y = -\frac{2}{3}x - \frac{13}{3} $ |
| 6 | $ y = -x + 3 $ |

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