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

To solve the problem of finding the slope and y-intercept for each equation, we need to rewrite each equation in the slope-intercept form, which is:

\[
y = mx + b
\]

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

Let's go through each equation step by step.

---

1) \(-5x + 4y = -16\)

Rewrite in slope-intercept form \( y = mx + b \):

\[
-5x + 4y = -16
\]

Add \( 5x \) to both sides:

\[
4y = 5x - 16
\]

Divide everything by 4:

\[
y = \frac{5}{4}x - 4
\]

So:
- Slope (\( m \)) = \(\frac{5}{4}\)
- Y-intercept (\( b \)) = \(-4\)

Answer:
\[
\text{slope} = \frac{5}{4}, \quad \text{y-intercept} = -4
\]

---

2) \( y = \frac{5}{2}x - 4 \)

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

- Slope (\( m \)) = \(\frac{5}{2}\)
- Y-intercept (\( b \)) = \(-4\)

Answer:
\[
\text{slope} = \frac{5}{2}, \quad \text{y-intercept} = -4
\]

---

3) \( 2x + 9y = 18 \)

Rewrite in slope-intercept form \( y = mx + b \):

\[
2x + 9y = 18
\]

Subtract \( 2x \) from both sides:

\[
9y = -2x + 18
\]

Divide everything by 9:

\[
y = -\frac{2}{9}x + 2
\]

So:
- Slope (\( m \)) = \(-\frac{2}{9}\)
- Y-intercept (\( b \)) = \(2\)

Answer:
\[
\text{slope} = -\frac{2}{9}, \quad \text{y-intercept} = 2
\]

---

4) \( -x + 4y = -16 \)

Rewrite in slope-intercept form \( y = mx + b \):

\[
-x + 4y = -16
\]

Add \( x \) to both sides:

\[
4y = x - 16
\]

Divide everything by 4:

\[
y = \frac{1}{4}x - 4
\]

So:
- Slope (\( m \)) = \(\frac{1}{4}\)
- Y-intercept (\( b \)) = \(-4\)

Answer:
\[
\text{slope} = \frac{1}{4}, \quad \text{y-intercept} = -4
\]

---

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

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

- Slope (\( m \)) = \(\frac{1}{2}\)
- Y-intercept (\( b \)) = \(-1\)

Answer:
\[
\text{slope} = \frac{1}{2}, \quad \text{y-intercept} = -1
\]

---

6) \( -6x + 5y = -10 \)

Rewrite in slope-intercept form \( y = mx + b \):

\[
-6x + 5y = -10
\]

Add \( 6x \) to both sides:

\[
5y = 6x - 10
\]

Divide everything by 5:

\[
y = \frac{6}{5}x - 2
\]

So:
- Slope (\( m \)) = \(\frac{6}{5}\)
- Y-intercept (\( b \)) = \(-2\)

Answer:
\[
\text{slope} = \frac{6}{5}, \quad \text{y-intercept} = -2
\]

---

7) \( y = -\frac{7}{8}x - 3 \)

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

- Slope (\( m \)) = \(-\frac{7}{8}\)
- Y-intercept (\( b \)) = \(-3\)

Answer:
\[
\text{slope} = -\frac{7}{8}, \quad \text{y-intercept} = -3
\]

---

8) \( -3x + 2y = 6 \)

Rewrite in slope-intercept form \( y = mx + b \):

\[
-3x + 2y = 6
\]

Add \( 3x \) to both sides:

\[
2y = 3x + 6
\]

Divide everything by 2:

\[
y = \frac{3}{2}x + 3
\]

So:
- Slope (\( m \)) = \(\frac{3}{2}\)
- Y-intercept (\( b \)) = \(3\)

Answer:
\[
\text{slope} = \frac{3}{2}, \quad \text{y-intercept} = 3
\]

---

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

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

- Slope (\( m \)) = \(\frac{3}{2}\)
- Y-intercept (\( b \)) = \(3\)

Answer:
\[
\text{slope} = \frac{3}{2}, \quad \text{y-intercept} = 3
\]

---

10) \( y = \frac{7}{4}x - 3 \)

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

- Slope (\( m \)) = \(\frac{7}{4}\)
- Y-intercept (\( b \)) = \(-3\)

Answer:
\[
\text{slope} = \frac{7}{4}, \quad \text{y-intercept} = -3
\]

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & \text{slope} = \frac{5}{4}, \quad \text{y-intercept} = -4 \\
2) & \text{slope} = \frac{5}{2}, \quad \text{y-intercept} = -4 \\
3) & \text{slope} = -\frac{2}{9}, \quad \text{y-intercept} = 2 \\
4) & \text{slope} = \frac{1}{4}, \quad \text{y-intercept} = -4 \\
5) & \text{slope} = \frac{1}{2}, \quad \text{y-intercept} = -1 \\
6) & \text{slope} = \frac{6}{5}, \quad \text{y-intercept} = -2 \\
7) & \text{slope} = -\frac{7}{8}, \quad \text{y-intercept} = -3 \\
8) & \text{slope} = \frac{3}{2}, \quad \text{y-intercept} = 3 \\
9) & \text{slope} = \frac{3}{2}, \quad \text{y-intercept} = 3 \\
10) & \text{slope} = \frac{7}{4}, \quad \text{y-intercept} = -3 \\
\end{array}
}
\]