Math worksheet for practicing finding slope and y-intercept of linear equations.

To solve the problem of finding the slope and y-intercept for each equation, we will use the slope-intercept form of a linear equation, which is:

\[
y = mx + b
\]

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

If an equation is not in this form, we will rearrange it to match \( y = mx + b \).

Let's solve each equation step by step.

---

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

This equation is already in the slope-intercept form \( y = mx + b \).

- Slope (\( m \)): 4
- y-intercept (\( b \)): 8

Answer:
- Slope: \( 4 \)
- y-intercept: \( 8 \)

---

2. \( y = \frac{1}{2}x - 1 \)

This equation is also in the slope-intercept form \( y = mx + b \).

- Slope (\( m \)): \( \frac{1}{2} \)
- y-intercept (\( b \)): \( -1 \)

Answer:
- Slope: \( \frac{1}{2} \)
- y-intercept: \( -1 \)

---

3. \( -7x = 14 - 9y \)

Rearrange the equation to isolate \( y \):

\[
-7x = 14 - 9y
\]

Add \( 9y \) to both sides:

\[
9y = 14 + 7x
\]

Divide everything by 9:

\[
y = \frac{7}{9}x + \frac{14}{9}
\]

Now, the equation is in the slope-intercept form \( y = mx + b \).

- Slope (\( m \)): \( \frac{7}{9} \)
- y-intercept (\( b \)): \( \frac{14}{9} \)

Answer:
- Slope: \( \frac{7}{9} \)
- y-intercept: \( \frac{14}{9} \)

---

4. \( y = \frac{2}{3}x + 3 \)

This equation is already in the slope-intercept form \( y = mx + b \).

- Slope (\( m \)): \( \frac{2}{3} \)
- y-intercept (\( b \)): 3

Answer:
- Slope: \( \frac{2}{3} \)
- y-intercept: \( 3 \)

---

5. \( y + 4x - 3 = 11 \)

Rearrange the equation to isolate \( y \):

\[
y + 4x - 3 = 11
\]

Add 3 to both sides:

\[
y + 4x = 14
\]

Subtract \( 4x \) from both sides:

\[
y = -4x + 14
\]

Now, the equation is in the slope-intercept form \( y = mx + b \).

- Slope (\( m \)): \( -4 \)
- y-intercept (\( b \)): 14

Answer:
- Slope: \( -4 \)
- y-intercept: \( 14 \)

---

6. \( 6x + 5y + 8 = 0 \)

Rearrange the equation to isolate \( y \):

\[
6x + 5y + 8 = 0
\]

Subtract \( 6x \) and 8 from both sides:

\[
5y = -6x - 8
\]

Divide everything by 5:

\[
y = -\frac{6}{5}x - \frac{8}{5}
\]

Now, the equation is in the slope-intercept form \( y = mx + b \).

- Slope (\( m \)): \( -\frac{6}{5} \)
- y-intercept (\( b \)): \( -\frac{8}{5} \)

Answer:
- Slope: \( -\frac{6}{5} \)
- y-intercept: \( -\frac{8}{5} \)

---

7. \( y = 6x + 16 \)

This equation is already in the slope-intercept form \( y = mx + b \).

- Slope (\( m \)): 6
- y-intercept (\( b \)): 16

Answer:
- Slope: \( 6 \)
- y-intercept: \( 16 \)

---

8. \( y = 6x + \frac{7}{2} \)

This equation is already in the slope-intercept form \( y = mx + b \).

- Slope (\( m \)): 6
- y-intercept (\( b \)): \( \frac{7}{2} \)

Answer:
- Slope: \( 6 \)
- y-intercept: \( \frac{7}{2} \)

---

9. \( y = x - 14 \)

This equation is already in the slope-intercept form \( y = mx + b \).

- Slope (\( m \)): 1
- y-intercept (\( b \)): \( -14 \)

Answer:
- Slope: \( 1 \)
- y-intercept: \( -14 \)

---

10. \( \frac{1}{3} = x + \frac{3y}{5} \)

Rearrange the equation to isolate \( y \):

\[
\frac{1}{3} = x + \frac{3y}{5}
\]

Subtract \( x \) from both sides:

\[
\frac{1}{3} - x = \frac{3y}{5}
\]

Multiply through by 5 to clear the fraction:

\[
5 \left( \frac{1}{3} - x \right) = 3y
\]

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

Divide everything by 3:

\[
y = -\frac{5}{3}x + \frac{5}{9}
\]

Now, the equation is in the slope-intercept form \( y = mx + b \).

- Slope (\( m \)): \( -\frac{5}{3} \)
- y-intercept (\( b \)): \( \frac{5}{9} \)

Answer:
- Slope: \( -\frac{5}{3} \)
- y-intercept: \( \frac{5}{9} \)

---

Final Answers:

1. Slope: \( 4 \), y-intercept: \( 8 \)
2. Slope: \( \frac{1}{2} \), y-intercept: \( -1 \)
3. Slope: \( \frac{7}{9} \), y-intercept: \( \frac{14}{9} \)
4. Slope: \( \frac{2}{3} \), y-intercept: \( 3 \)
5. Slope: \( -4 \), y-intercept: \( 14 \)
6. Slope: \( -\frac{6}{5} \), y-intercept: \( -\frac{8}{5} \)
7. Slope: \( 6 \), y-intercept: \( 16 \)
8. Slope: \( 6 \), y-intercept: \( \frac{7}{2} \)
9. Slope: \( 1 \), y-intercept: \( -14 \)
10. Slope: \( -\frac{5}{3} \), y-intercept: \( \frac{5}{9} \)

\boxed{
\begin{array}{ll}
1. & \text{Slope: } 4, \text{ y-intercept: } 8 \\
2. & \text{Slope: } \frac{1}{2}, \text{ y-intercept: } -1 \\
3. & \text{Slope: } \frac{7}{9}, \text{ y-intercept: } \frac{14}{9} \\
4. & \text{Slope: } \frac{2}{3}, \text{ y-intercept: } 3 \\
5. & \text{Slope: } -4, \text{ y-intercept: } 14 \\
6. & \text{Slope: } -\frac{6}{5}, \text{ y-intercept: } -\frac{8}{5} \\
7. & \text{Slope: } 6, \text{ y-intercept: } 16 \\
8. & \text{Slope: } 6, \text{ y-intercept: } \frac{7}{2} \\
9. & \text{Slope: } 1, \text{ y-intercept: } -14 \\
10. & \text{Slope: } -\frac{5}{3}, \text{ y-intercept: } \frac{5}{9} \\
\end{array}
}