Convert linear equations from standard form to slope-intercept form in this math worksheet.

To convert a linear equation from standard form to slope-intercept form, we need to solve for \( y \) in terms of \( x \). The slope-intercept form is given by:

\[
y = mx + b
\]

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

Let's go through each equation step by step.

---

1. \( x + 5y = 5 \)

1. Start with the equation:
\[
x + 5y = 5
\]

2. Subtract \( x \) from both sides:
\[
5y = -x + 5
\]

3. Divide every term by 5:
\[
y = -\frac{1}{5}x + 1
\]

So, the slope-intercept form is:
\[
\boxed{y = -\frac{1}{5}x + 1}
\]

---

2. \( 3x + 2y = 4 \)

1. Start with the equation:
\[
3x + 2y = 4
\]

2. Subtract \( 3x \) from both sides:
\[
2y = -3x + 4
\]

3. Divide every term by 2:
\[
y = -\frac{3}{2}x + 2
\]

So, the slope-intercept form is:
\[
\boxed{y = -\frac{3}{2}x + 2}
\]

---

3. \( 2x + y = 4 \)

1. Start with the equation:
\[
2x + y = 4
\]

2. Subtract \( 2x \) from both sides:
\[
y = -2x + 4
\]

So, the slope-intercept form is:
\[
\boxed{y = -2x + 4}
\]

---

4. \( 4x - 2y = 6 \)

1. Start with the equation:
\[
4x - 2y = 6
\]

2. Subtract \( 4x \) from both sides:
\[
-2y = -4x + 6
\]

3. Divide every term by \(-2\):
\[
y = 2x - 3
\]

So, the slope-intercept form is:
\[
\boxed{y = 2x - 3}
\]

---

5. \( 8x - 4y = 16 \)

1. Start with the equation:
\[
8x - 4y = 16
\]

2. Subtract \( 8x \) from both sides:
\[
-4y = -8x + 16
\]

3. Divide every term by \(-4\):
\[
y = 2x - 4
\]

So, the slope-intercept form is:
\[
\boxed{y = 2x - 4}
\]

---

6. \( 3x + 4y = 4 \)

1. Start with the equation:
\[
3x + 4y = 4
\]

2. Subtract \( 3x \) from both sides:
\[
4y = -3x + 4
\]

3. Divide every term by 4:
\[
y = -\frac{3}{4}x + 1
\]

So, the slope-intercept form is:
\[
\boxed{y = -\frac{3}{4}x + 1}
\]

---

7. \( 9x - 4y = -16 \)

1. Start with the equation:
\[
9x - 4y = -16
\]

2. Subtract \( 9x \) from both sides:
\[
-4y = -9x - 16
\]

3. Divide every term by \(-4\):
\[
y = \frac{9}{4}x + 4
\]

So, the slope-intercept form is:
\[
\boxed{y = \frac{9}{4}x + 4}
\]

---

8. \( 2x - 5y = 10 \)

1. Start with the equation:
\[
2x - 5y = 10
\]

2. Subtract \( 2x \) from both sides:
\[
-5y = -2x + 10
\]

3. Divide every term by \(-5\):
\[
y = \frac{2}{5}x - 2
\]

So, the slope-intercept form is:
\[
\boxed{y = \frac{2}{5}x - 2}
\]

---

9. \( 3x + 5y = -25 \)

1. Start with the equation:
\[
3x + 5y = -25
\]

2. Subtract \( 3x \) from both sides:
\[
5y = -3x - 25
\]

3. Divide every term by 5:
\[
y = -\frac{3}{5}x - 5
\]

So, the slope-intercept form is:
\[
\boxed{y = -\frac{3}{5}x - 5}
\]

---

10. \( 7x - y = 4 \)

1. Start with the equation:
\[
7x - y = 4
\]

2. Subtract \( 7x \) from both sides:
\[
-y = -7x + 4
\]

3. Multiply every term by \(-1\):
\[
y = 7x - 4
\]

So, the slope-intercept form is:
\[
\boxed{y = 7x - 4}
\]

---

Final Answers:

1. \( y = -\frac{1}{5}x + 1 \)
2. \( y = -\frac{3}{2}x + 2 \)
3. \( y = -2x + 4 \)
4. \( y = 2x - 3 \)
5. \( y = 2x - 4 \)
6. \( y = -\frac{3}{4}x + 1 \)
7. \( y = \frac{9}{4}x + 4 \)
8. \( y = \frac{2}{5}x - 2 \)
9. \( y = -\frac{3}{5}x - 5 \)
10. \( y = 7x - 4 \)

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