Writing a Linear Equation from the Slope and a Point (A) - Free Printable

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

$$
y - y_1 = m(x - x_1)
$$

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

We'll write the equation in point-slope form and then solve for $ y $ to get it into slope-intercept form: $ y = mx + b $.

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1. Slope: $-4$, Point: $(-1, -3)$

Point-Slope Form:
$$
y - (-3) = -4(x - (-1)) \Rightarrow y + 3 = -4(x + 1)
$$

Solve for $ y $:
$$
y + 3 = -4x - 4 \\
y = -4x - 4 - 3 \\
\boxed{y = -4x - 7}
$$

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2. Slope: $-\frac{1}{3}$, Point: $(-9, 6)$

Point-Slope Form:
$$
y - 6 = -\frac{1}{3}(x + 9)
$$

Solve for $ y $:
$$
y - 6 = -\frac{1}{3}x - 3 \\
y = -\frac{1}{3}x - 3 + 6 \\
\boxed{y = -\frac{1}{3}x + 3}
$$

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3. Slope: $3$, Point: $(1, -1)$

Point-Slope Form:
$$
y - (-1) = 3(x - 1) \Rightarrow y + 1 = 3(x - 1)
$$

Solve for $ y $:
$$
y + 1 = 3x - 3 \\
y = 3x - 3 - 1 \\
\boxed{y = 3x - 4}
$$

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4. Slope: $-\frac{11}{4}$, Point: $(4, -4)$

Point-Slope Form:
$$
y - (-4) = -\frac{11}{4}(x - 4) \Rightarrow y + 4 = -\frac{11}{4}(x - 4)
$$

Solve for $ y $:
$$
y + 4 = -\frac{11}{4}x + 11 \\
y = -\frac{11}{4}x + 11 - 4 \\
\boxed{y = -\frac{11}{4}x + 7}
$$

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5. Slope: undefined, Point: $(-4, 8)$

Undefined slope means the line is vertical.

Vertical lines have equations of the form:
$$
x = \text{constant}
$$

Since the point is $(-4, 8)$, the equation is:
$$
\boxed{x = -4}
$$

> Note: This cannot be written in slope-intercept form because vertical lines have no defined slope and are not functions.

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6. Slope: $\frac{10}{9}$, Point: $(-9, -9)$

Point-Slope Form:
$$
y - (-9) = \frac{10}{9}(x + 9) \Rightarrow y + 9 = \frac{10}{9}(x + 9)
$$

Solve for $ y $:
$$
y + 9 = \frac{10}{9}x + 10 \\
y = \frac{10}{9}x + 10 - 9 \\
\boxed{y = \frac{10}{9}x + 1}
$$

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7. Slope: $\frac{4}{7}$, Point: $(7, -3)$

Point-Slope Form:
$$
y - (-3) = \frac{4}{7}(x - 7) \Rightarrow y + 3 = \frac{4}{7}(x - 7)
$$

Solve for $ y $:
$$
y + 3 = \frac{4}{7}x - 4 \\
y = \frac{4}{7}x - 4 - 3 \\
\boxed{y = \frac{4}{7}x - 7}
$$

---

8. Slope: $\frac{3}{4}$, Point: $(-4, 6)$

Point-Slope Form:
$$
y - 6 = \frac{3}{4}(x + 4)
$$

Solve for $ y $:
$$
y - 6 = \frac{3}{4}x + 3 \\
y = \frac{3}{4}x + 3 + 6 \\
\boxed{y = \frac{3}{4}x + 9}
$$

---

9. Slope: $-\frac{4}{3}$, Point: $(-9, 5)$

Point-Slope Form:
$$
y - 5 = -\frac{4}{3}(x + 9)
$$

Solve for $ y $:
$$
y - 5 = -\frac{4}{3}x - 12 \\
y = -\frac{4}{3}x - 12 + 5 \\
\boxed{y = -\frac{4}{3}x - 7}
$$

---

10. Slope: $-\frac{13}{4}$, Point: $(4, -8)$

Point-Slope Form:
$$
y - (-8) = -\frac{13}{4}(x - 4) \Rightarrow y + 8 = -\frac{13}{4}(x - 4)
$$

Solve for $ y $:
$$
y + 8 = -\frac{13}{4}x + 13 \\
y = -\frac{13}{4}x + 13 - 8 \\
\boxed{y = -\frac{13}{4}x + 5}
$$

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✔ Final Answers Summary:

| Problem | Equation in Point-Slope Form | Equation Solved for $ y $ |
|--------|-------------------------------|-----------------------------|
| 1 | $ y + 3 = -4(x + 1) $ | $ y = -4x - 7 $ |
| 2 | $ y - 6 = -\frac{1}{3}(x + 9) $ | $ y = -\frac{1}{3}x + 3 $ |
| 3 | $ y + 1 = 3(x - 1) $ | $ y = 3x - 4 $ |
| 4 | $ y + 4 = -\frac{11}{4}(x - 4) $ | $ y = -\frac{11}{4}x + 7 $ |
| 5 | $ x = -4 $ | $ x = -4 $ (vertical line) |
| 6 | $ y + 9 = \frac{10}{9}(x + 9) $ | $ y = \frac{10}{9}x + 1 $ |
| 7 | $ y + 3 = \frac{4}{7}(x - 7) $ | $ y = \frac{4}{7}x - 7 $ |
| 8 | $ y - 6 = \frac{3}{4}(x + 4) $ | $ y = \frac{3}{4}x + 9 $ |
| 9 | $ y - 5 = -\frac{4}{3}(x + 9) $ | $ y = -\frac{4}{3}x - 7 $ |
| 10 | $ y + 8 = -\frac{13}{4}(x - 4) $ | $ y = -\frac{13}{4}x + 5 $ |

Let me know if you'd like these graphed or explained further!