Slope-intercept form answer key for a math worksheet, showing equations and their solutions.

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 for Each Equation

#### 1. \( 3x + 4y = 8 \)
To convert to slope-intercept form, solve for \( y \):

\[
3x + 4y = 8
\]
Subtract \( 3x \) from both sides:
\[
4y = -3x + 8
\]
Divide by 4:
\[
y = -\frac{3}{4}x + 2
\]

Answer: \( y = -\frac{3}{4}x + 2 \)

---

#### 2. \( 9x + 35 = -5y \)
Rearrange to isolate \( y \):

\[
9x + 35 = -5y
\]
Divide by \(-5\):
\[
y = -\frac{9}{5}x - 7
\]

Answer: \( y = -\frac{9}{5}x - 7 \)

---

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

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

Answer: \( y = -3x + 3 \)

---

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

\[
-11x - 7y = -56
\]
Add \( 11x \) to both sides:
\[
-7y = 11x - 56
\]
Divide by \(-7\):
\[
y = -\frac{11}{7}x + 8
\]

Answer: \( y = -\frac{11}{7}x + 8 \)

---

#### 5. \( \frac{5}{3}y = -(x - 5) \)
Simplify and solve for \( y \):

\[
\frac{5}{3}y = -(x - 5)
\]
Distribute the negative sign:
\[
\frac{5}{3}y = -x + 5
\]
Multiply through by \(\frac{3}{5}\):
\[
y = -\frac{3}{5}x + 3
\]

Answer: \( y = -\frac{3}{5}x + 3 \)

---

#### 6. \( -2(2x + y) = 28 \)
Expand and solve for \( y \):

\[
-2(2x + y) = 28
\]
Distribute \(-2\):
\[
-4x - 2y = 28
\]
Add \( 4x \) to both sides:
\[
-2y = 4x + 28
\]
Divide by \(-2\):
\[
y = -2x - 14
\]

Answer: \( y = -2x - 14 \)

---

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

\[
-14x + y = 7
\]
Add \( 14x \) to both sides:
\[
y = 14x + 7
\]

Answer: \( y = 14x + 7 \)

---

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

\[
12y = \frac{8x - 48}{3}
\]
Divide both sides by 12:
\[
y = \frac{8x - 48}{3 \cdot 12}
\]
Simplify the denominator:
\[
y = \frac{8x - 48}{36}
\]
Separate the terms:
\[
y = \frac{8x}{36} - \frac{48}{36}
\]
Simplify fractions:
\[
y = \frac{2}{9}x - \frac{4}{3}
\]

Answer: \( y = \frac{2}{9}x - \frac{4}{3} \)

---

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

\[
\frac{3(x - y)}{2} = 9
\]
Multiply through by 2:
\[
3(x - y) = 18
\]
Divide by 3:
\[
x - y = 6
\]
Subtract \( x \) from both sides:
\[
-y = -x + 6
\]
Multiply by \(-1\):
\[
y = x - 6
\]

Answer: \( y = x - 6 \)

---

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

\[
\frac{2}{3}x + 4(y - 2) = 0
\]
Distribute the 4:
\[
\frac{2}{3}x + 4y - 8 = 0
\]
Add 8 to both sides:
\[
\frac{2}{3}x + 4y = 8
\]
Subtract \(\frac{2}{3}x\) from both sides:
\[
4y = -\frac{2}{3}x + 8
\]
Divide by 4:
\[
y = -\frac{2}{3 \cdot 4}x + \frac{8}{4}
\]
Simplify:
\[
y = -\frac{1}{6}x + 2
\]

Answer: \( y = -\frac{1}{6}x + 2 \)

---

Final Answer:

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