Slope Intercept Form Worksheets with Answer Key - Free Printable

Let's solve each of these problems by rewriting the given equations in slope-intercept form, which is:

$$
y = mx + b
$$

where:
- $ m $ is the slope,
- $ b $ is the y-intercept.

We'll go through each equation one by one, solving for $ y $.

---

1. $ 4x - y = 2 $

Solve for $ y $:
$$
-y = -4x + 2 \\
y = 4x - 2
$$

✔ Answer: $ y = 4x - 2 $

---

2. $ x - 2y = 6 $

Solve for $ y $:
$$
-2y = -x + 6 \\
y = \frac{1}{2}x - 3
$$

✔ Answer: $ y = \frac{1}{2}x - 3 $

---

3. $ y + 1 = 3(x + 2) $

Distribute and simplify:
$$
y + 1 = 3x + 6 \\
y = 3x + 5
$$

✔ Answer: $ y = 3x + 5 $

---

4. $ 5y + 10 = -2x $

Solve for $ y $:
$$
5y = -2x - 10 \\
y = -\frac{2}{5}x - 2
$$

✔ Answer: $ y = -\frac{2}{5}x - 2 $

---

5. $ 11x - 4y = 32 $

Solve for $ y $:
$$
-4y = -11x + 32 \\
y = \frac{11}{4}x - 8
$$

✔ Answer: $ y = \frac{11}{4}x - 8 $

---

6. $ x + y = -15 $

Solve for $ y $:
$$
y = -x - 15
$$

✔ Answer: $ y = -x - 15 $

---

7. $ -5 - y = -3x $

Solve for $ y $:
$$
-y = -3x + 5 \\
y = 3x - 5
$$

✔ Answer: $ y = 3x - 5 $

---

8. $ x - 6y = 0 $

Solve for $ y $:
$$
-6y = -x \\
y = \frac{1}{6}x
$$

✔ Answer: $ y = \frac{1}{6}x $

---

9. $ -14x + y = 7 $

Solve for $ y $:
$$
y = 14x + 7
$$

✔ Answer: $ y = 14x + 7 $

---

10. $ y + 1 = 3(x + 2) $

Same as #3:
$$
y + 1 = 3x + 6 \\
y = 3x + 5
$$

✔ Answer: $ y = 3x + 5 $

---

11. $ 6 - 2y = -x $

Solve for $ y $:
$$
-2y = -x - 6 \\
y = \frac{1}{2}x + 3
$$

✔ Answer: $ y = \frac{1}{2}x + 3 $

---

12. $ 4y = 7x + 33 $

Solve for $ y $:
$$
y = \frac{7}{4}x + \frac{33}{4}
$$

✔ Answer: $ y = \frac{7}{4}x + \frac{33}{4} $

---

13. $ 3y - 2x = 9 $

Solve for $ y $:
$$
3y = 2x + 9 \\
y = \frac{2}{3}x + 3
$$

✔ Answer: $ y = \frac{2}{3}x + 3 $

---

14. $ 2(x + y) = 8 $

Distribute:
$$
2x + 2y = 8 \\
2y = -2x + 8 \\
y = -x + 4
$$

✔ Answer: $ y = -x + 4 $

---

15. $ \frac{6y}{y + 8} = 3 $

This one is not a linear equation in standard form. Let's solve it carefully.

Given:
$$
\frac{6y}{y + 8} = 3
$$

Multiply both sides by $ y + 8 $ (assuming $ y \ne -8 $):
$$
6y = 3(y + 8) \\
6y = 3y + 24 \\
3y = 24 \\
y = 8
$$

But this gives a single solution, not an equation of a line. So this is not a linear equation in two variables — it's a rational equation.

However, the goal was to write equations in slope-intercept form, which applies only to linear equations with two variables.

So, this equation cannot be written in slope-intercept form because it’s not a linear equation in $ x $ and $ y $. It only involves $ y $, and solving it yields a single value: $ y = 8 $.

But if we interpret this as a horizontal line at $ y = 8 $, then:

$$
y = 0x + 8
$$

So technically, it can be written in slope-intercept form as:

✔ Answer: $ y = 8 $

(Note: This is a horizontal line with slope 0.)

---

## ✔ Final Answers:

| Problem | Slope-Intercept Form |
|--------|-----------------------|
| 1 | $ y = 4x - 2 $ |
| 2 | $ y = \frac{1}{2}x - 3 $ |
| 3 | $ y = 3x + 5 $ |
| 4 | $ y = -\frac{2}{5}x - 2 $ |
| 5 | $ y = \frac{11}{4}x - 8 $ |
| 6 | $ y = -x - 15 $ |
| 7 | $ y = 3x - 5 $ |
| 8 | $ y = \frac{1}{6}x $ |
| 9 | $ y = 14x + 7 $ |
| 10 | $ y = 3x + 5 $ |
| 11 | $ y = \frac{1}{2}x + 3 $ |
| 12 | $ y = \frac{7}{4}x + \frac{33}{4} $ |
| 13 | $ y = \frac{2}{3}x + 3 $ |
| 14 | $ y = -x + 4 $ |
| 15 | $ y = 8 $ |

> 🔍 Note: Problem 15 is not a typical linear equation in two variables, but since it simplifies to a constant $ y = 8 $, it represents a horizontal line and can be expressed in slope-intercept form.

---

Let me know if you'd like this formatted as a printable worksheet or need explanations for any step!