Slope Intercept Form Worksheets with Answer Key - Free Printable

Let's solve each problem step by step, rewriting the equations in slope-intercept form:
$$
y = mx + b
$$
where $ m $ is the slope and $ b $ is the y-intercept.

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Part 1: Rewrite equations into slope-intercept form

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#### 1. $ 2y = -1x - 6 $

Step 1: Divide both sides by 2 to isolate $ y $:
$$
y = \frac{-1x - 6}{2}
$$
$$
y = -\frac{1}{2}x - 3
$$

✔ Answer: $ y = -\frac{1}{2}x - 3 $

---

#### 2. $ y - 4x = 8 $

Step 1: Add $ 4x $ to both sides:
$$
y = 4x + 8
$$

✔ Answer: $ y = 4x + 8 $

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#### 3. $ 0.8x + 0.4y = 1.2 $

Step 1: Subtract $ 0.8x $ from both sides:
$$
0.4y = -0.8x + 1.2
$$

Step 2: Divide every term by 0.4:
$$
y = \frac{-0.8}{0.4}x + \frac{1.2}{0.4}
$$
$$
y = -2x + 3
$$

✔ Answer: $ y = -2x + 3 $

---

#### 4. $ x + 6y = 4 $

Step 1: Subtract $ x $ from both sides:
$$
6y = -x + 4
$$

Step 2: Divide by 6:
$$
y = -\frac{1}{6}x + \frac{4}{6}
$$
$$
y = -\frac{1}{6}x + \frac{2}{3}
$$

✔ Answer: $ y = -\frac{1}{6}x + \frac{2}{3} $

---

#### 5. $ -x - y = -2 $

Step 1: Add $ x $ to both sides:
$$
- y = x - 2
$$

Step 2: Multiply both sides by $-1$:
$$
y = -x + 2
$$

✔ Answer: $ y = -x + 2 $

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#### 6. $ y - 1 = \frac{2}{3}(x + 3) $

Step 1: Distribute $ \frac{2}{3} $:
$$
y - 1 = \frac{2}{3}x + 2
$$

Step 2: Add 1 to both sides:
$$
y = \frac{2}{3}x + 3
$$

✔ Answer: $ y = \frac{2}{3}x + 3 $

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Part 2: Write equations given slope and a point

Use point-slope form:
$$
y - y_1 = m(x - x_1)
$$
Then convert to slope-intercept form.

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#### 7. Slope = $ -\frac{4}{7} $, through (14, 3)

Step 1: Use point-slope:
$$
y - 3 = -\frac{4}{7}(x - 14)
$$

Step 2: Distribute:
$$
y - 3 = -\frac{4}{7}x + \frac{56}{7}
$$
$$
y - 3 = -\frac{4}{7}x + 8
$$

Step 3: Add 3:
$$
y = -\frac{4}{7}x + 11
$$

✔ Answer: $ y = -\frac{4}{7}x + 11 $

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#### 8. Slope = 3, through (-5, 6)

Step 1: Point-slope:
$$
y - 6 = 3(x + 5)
$$

Step 2: Distribute:
$$
y - 6 = 3x + 15
$$

Step 3: Add 6:
$$
y = 3x + 21
$$

✔ Answer: $ y = 3x + 21 $

---

#### 9. Slope = -4, through (-2, 5)

Step 1: Point-slope:
$$
y - 5 = -4(x + 2)
$$

Step 2: Distribute:
$$
y - 5 = -4x - 8
$$

Step 3: Add 5:
$$
y = -4x - 3
$$

✔ Answer: $ y = -4x - 3 $

---

#### 10. Slope = $ \frac{5}{3} $, through (3, 5)

Step 1: Point-slope:
$$
y - 5 = \frac{5}{3}(x - 3)
$$

Step 2: Distribute:
$$
y - 5 = \frac{5}{3}x - 5
$$

Step 3: Add 5:
$$
y = \frac{5}{3}x
$$

✔ Answer: $ y = \frac{5}{3}x $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ y = -\frac{1}{2}x - 3 $ |
| 2 | $ y = 4x + 8 $ |
| 3 | $ y = -2x + 3 $ |
| 4 | $ y = -\frac{1}{6}x + \frac{2}{3} $ |
| 5 | $ y = -x + 2 $ |
| 6 | $ y = \frac{2}{3}x + 3 $ |
| 7 | $ y = -\frac{4}{7}x + 11 $ |
| 8 | $ y = 3x + 21 $ |
| 9 | $ y = -4x - 3 $ |
| 10 | $ y = \frac{5}{3}x $ |

Let me know if you'd like these explained with graphs or visual steps!