Comprehensive worksheet featuring 28 problems on rearranging literal equations into the slope-intercept form y = mx + c.

Let's solve each equation in Section A and Section B by rearranging them into the form:

$$
y = mx + c
$$

This is the slope-intercept form of a linear equation, where:
- $ m $ is the slope,
- $ c $ is the y-intercept.

We'll go step-by-step for each problem.

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✔ Section A: Rearranging to $ y = mx + c $

#### 1) $ y - 8 = 4x $
Add 8 to both sides:
$$
y = 4x + 8
$$

#### 2) $ 6 + y = 7x $
Subtract 6 from both sides:
$$
y = 7x - 6
$$

#### 3) $ 2x + y = 3 $
Subtract $ 2x $ from both sides:
$$
y = -2x + 3
$$

#### 4) $ y + 4x = 5 $
Subtract $ 4x $ from both sides:
$$
y = -4x + 5
$$

#### 5) $ 3x + y = -5 $
Subtract $ 3x $ from both sides:
$$
y = -3x - 5
$$

#### 6) $ y + 5x = 0 $
Subtract $ 5x $ from both sides:
$$
y = -5x
$$

#### 7) $ 7 + y = -2x $
Subtract 7 from both sides:
$$
y = -2x - 7
$$

#### 8) $ -4x + y = 8 $
Add $ 4x $ to both sides:
$$
y = 4x + 8
$$

#### 9) $ y - 5 = 12x $
Add 5 to both sides:
$$
y = 12x + 5
$$

#### 10) $ y - 2x = -4 $
Add $ 2x $ to both sides:
$$
y = 2x - 4
$$

#### 11) $ 3 - y = x $
Subtract 3 from both sides:
$$
-y = x - 3
$$
Multiply both sides by -1:
$$
y = -x + 3
$$

#### 12) $ 5x - y = 9 $
Subtract $ 5x $ from both sides:
$$
-y = -5x + 9
$$
Multiply both sides by -1:
$$
y = 5x - 9
$$

#### 13) $ -y + 15 = -4x $
Subtract 15 from both sides:
$$
-y = -4x - 15
$$
Multiply both sides by -1:
$$
y = 4x + 15
$$

#### 14) $ -3x - y = 10 $
Add $ 3x $ to both sides:
$$
-y = 3x + 10
$$
Multiply both sides by -1:
$$
y = -3x - 10
$$

---

✔ Section B: Rearranging to $ y = mx + c $

These equations have coefficients on $ y $, so we need to divide both sides by that coefficient after isolating $ y $.

#### 1) $ 2y = 8 + 12x $
Divide both sides by 2:
$$
y = 4 + 6x \quad \Rightarrow \quad y = 6x + 4
$$

#### 2) $ 3y = 15x - 3 $
Divide both sides by 3:
$$
y = 5x - 1
$$

#### 3) $ 5y = 10 - 2x $
Divide both sides by 5:
$$
y = 2 - \frac{2}{5}x \quad \Rightarrow \quad y = -\frac{2}{5}x + 2
$$

#### 4) $ 3y = 4 + 7x $
Divide both sides by 3:
$$
y = \frac{4}{3} + \frac{7}{3}x \quad \Rightarrow \quad y = \frac{7}{3}x + \frac{4}{3}
$$

#### 5) $ 4y = 6x - 14 $
Divide both sides by 4:
$$
y = \frac{6}{4}x - \frac{14}{4} = \frac{3}{2}x - \frac{7}{2}
$$

#### 6) $ 6y = -3x + 9 $
Divide both sides by 6:
$$
y = -\frac{3}{6}x + \frac{9}{6} = -\frac{1}{2}x + \frac{3}{2}
$$

#### 7) $ 9y = 4x - 27 $
Divide both sides by 9:
$$
y = \frac{4}{9}x - 3
$$

#### 8) $ -4y = 12 + 8x $
Divide both sides by -4:
$$
y = \frac{12}{-4} + \frac{8x}{-4} = -3 - 2x \quad \Rightarrow \quad y = -2x - 3
$$

#### 9) $ -2y = x + 4 $
Divide both sides by -2:
$$
y = -\frac{1}{2}x - 2
$$

#### 10) $ -3y = 5 - 2x $
Divide both sides by -3:
$$
y = -\frac{5}{3} + \frac{2}{3}x \quad \Rightarrow \quad y = \frac{2}{3}x - \frac{5}{3}
$$

#### 11) $ -8y = 16x + 4 $
Divide both sides by -8:
$$
y = -2x - \frac{1}{2}
$$

#### 12) $ -2y = 10x - 3 $
Divide both sides by -2:
$$
y = -5x + \frac{3}{2}
$$

#### 13) $ -4y = -6 - 10x $
Divide both sides by -4:
$$
y = \frac{-6}{-4} + \frac{-10x}{-4} = \frac{3}{2} + \frac{5}{2}x \quad \Rightarrow \quad y = \frac{5}{2}x + \frac{3}{2}
$$

#### 14) $ -12y = 15x - 21 $
Divide both sides by -12:
$$
y = -\frac{15}{12}x + \frac{21}{12} = -\frac{5}{4}x + \frac{7}{4}
$$

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✔ Final Answers Summary

#### Section A
1. $ y = 4x + 8 $
2. $ y = 7x - 6 $
3. $ y = -2x + 3 $
4. $ y = -4x + 5 $
5. $ y = -3x - 5 $
6. $ y = -5x $
7. $ y = -2x - 7 $
8. $ y = 4x + 8 $
9. $ y = 12x + 5 $
10. $ y = 2x - 4 $
11. $ y = -x + 3 $
12. $ y = 5x - 9 $
13. $ y = 4x + 15 $
14. $ y = -3x - 10 $

#### Section B
1. $ y = 6x + 4 $
2. $ y = 5x - 1 $
3. $ y = -\frac{2}{5}x + 2 $
4. $ y = \frac{7}{3}x + \frac{4}{3} $
5. $ y = \frac{3}{2}x - \frac{7}{2} $
6. $ y = -\frac{1}{2}x + \frac{3}{2} $
7. $ y = \frac{4}{9}x - 3 $
8. $ y = -2x - 3 $
9. $ y = -\frac{1}{2}x - 2 $
10. $ y = \frac{2}{3}x - \frac{5}{3} $
11. $ y = -2x - \frac{1}{2} $
12. $ y = -5x + \frac{3}{2} $
13. $ y = \frac{5}{2}x + \frac{3}{2} $
14. $ y = -\frac{5}{4}x + \frac{7}{4} $

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🔍 Explanation of Strategy

To rewrite any equation in the form $ y = mx + c $:

1. Isolate $ y $ on one side.
2. Move all terms with $ x $ and constants to the other side.
3. If $ y $ has a coefficient (like $ 2y $), divide every term by that coefficient.
4. Simplify fractions if needed.

This process helps us identify the slope ($ m $) and y-intercept ($ c $), which are essential for graphing and understanding linear relationships.

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