Slope-intercept Form Exercises Worksheet - Free Printable

The task is to convert each given equation into slope-intercept form, which is written as:

\[
y = mx + b
\]

where:
- \( m \) is the slope,
- \( b \) is the y-intercept.

Solution Explanation

We will solve each equation step by step to rewrite it in the form \( y = mx + b \).

---

#### 1. \( 3x + 4y = 8 \)

1. Isolate \( y \):
\[
4y = -3x + 8
\]
2. Divide by 4:
\[
y = -\frac{3}{4}x + 2
\]

Answer:
\[
y = -\frac{3}{4}x + 2
\]

---

#### 2. \( 9x + 35 = -5y \)

1. Rearrange to isolate \( y \):
\[
-5y = -9x - 35
\]
2. Divide by \(-5\):
\[
y = \frac{-9x - 35}{-5} = \frac{9}{5}x + 7
\]

Answer:
\[
y = -\frac{9}{5}x - 7
\]

---

#### 3. \( 2y - 6 = -6x \)

1. Add 6 to both sides:
\[
2y = -6x + 6
\]
2. Divide by 2:
\[
y = -3x + 3
\]

Answer:
\[
y = -3x + 3
\]

---

#### 4. \( -11x - 7y = -56 \)

1. Isolate \( y \):
\[
-7y = 11x - 56
\]
2. Divide by \(-7\):
\[
y = \frac{11x - 56}{-7} = -\frac{11}{7}x + 8
\]

Answer:
\[
y = -\frac{11}{7}x + 8
\]

---

#### 5. \( \frac{5}{3}y = -(x - 5) \)

1. Simplify the right-hand side:
\[
\frac{5}{3}y = -x + 5
\]
2. Multiply through by \(\frac{3}{5}\):
\[
y = \frac{3}{5}(-x + 5) = -\frac{3}{5}x + 3
\]

Answer:
\[
y = -\frac{3}{5}x + 3
\]

---

#### 6. \( -2(2x + y) = 28 \)

1. Distribute \(-2\):
\[
-4x - 2y = 28
\]
2. Isolate \( y \):
\[
-2y = 4x + 28
\]
3. Divide by \(-2\):
\[
y = \frac{4x + 28}{-2} = -2x - 14
\]

Answer:
\[
y = -2x - 14
\]

---

#### 7. \( -14x + y = 7 \)

1. Isolate \( y \):
\[
y = 14x + 7
\]

Answer:
\[
y = 14x + 7
\]

---

#### 8. \( 12y = \frac{8x - 48}{3} \)

1. Simplify the right-hand side:
\[
12y = \frac{8x}{3} - \frac{48}{3} = \frac{8x}{3} - 16
\]
2. Divide through by 12:
\[
y = \frac{\frac{8x}{3} - 16}{12} = \frac{8x}{36} - \frac{16}{12} = \frac{2x}{9} - \frac{4}{3}
\]

Answer:
\[
y = \frac{2}{9}x - \frac{4}{3}
\]

---

#### 9. \( \frac{3(x - y)}{2} = 9 \)

1. Eliminate the fraction by multiplying through by 2:
\[
3(x - y) = 18
\]
2. Distribute 3:
\[
3x - 3y = 18
\]
3. Isolate \( y \):
\[
-3y = -3x + 18
\]
4. Divide by \(-3\):
\[
y = x - 6
\]

Answer:
\[
y = x - 6
\]

---

#### 10. \( \frac{2}{3}x + 4(y - 2) = 0 \)

1. Distribute 4:
\[
\frac{2}{3}x + 4y - 8 = 0
\]
2. Isolate \( y \):
\[
4y = -\frac{2}{3}x + 8
\]
3. Divide by 4:
\[
y = \frac{-\frac{2}{3}x + 8}{4} = -\frac{2}{3} \cdot \frac{x}{4} + \frac{8}{4} = -\frac{1}{6}x + 2
\]

Answer:
\[
y = -\frac{1}{6}x + 2
\]

---

Final Answer:

\[
\boxed{
\begin{aligned}
1. & \quad y = -\frac{3}{4}x + 2 \\
2. & \quad y = -\frac{9}{5}x - 7 \\
3. & \quad y = -3x + 3 \\
4. & \quad y = -\frac{11}{7}x + 8 \\
5. & \quad y = -\frac{3}{5}x + 3 \\
6. & \quad y = -2x - 14 \\
7. & \quad y = 14x + 7 \\
8. & \quad y = \frac{2}{9}x - \frac{4}{3} \\
9. & \quad y = x - 6 \\
10. & \quad y = -\frac{1}{6}x + 2
\end{aligned}
}
\]