Printable math worksheet for finding x-intercepts and y-intercepts of linear equations.

Sure! Let’s solve each problem step by step.

---

What are x-intercept and y-intercept?

- x-intercept: The point where the graph crosses the x-axis → set y = 0 and solve for x.
- y-intercept: The point where the graph crosses the y-axis → set x = 0 and solve for y.

We’ll apply this to each equation.

---

## Problem 1: –33y + 66x = –132

x-intercept (set y = 0):

–33(0) + 66x = –132
→ 66x = –132
→ x = –132 / 66 = –2

✔ x-intercept: –2

y-intercept (set x = 0):

–33y + 66(0) = –132
→ –33y = –132
→ y = –132 / –33 = 4

✔ y-intercept: 4

---

## Problem 2: 6 = x – 3y

Rewrite as: x – 3y = 6

x-intercept (y = 0):

x – 3(0) = 6 → x = 6

✔ x-intercept: 6

y-intercept (x = 0):

0 – 3y = 6 → –3y = 6 → y = –2

✔ y-intercept: –2

---

## Problem 3: 72 + 9y = –9x

Rewrite: 9y + 9x = –72 → divide all terms by 9: y + x = –8

Or keep original:

x-intercept (y = 0):

72 + 9(0) = –9x → 72 = –9x → x = 72 / –9 = –8

✔ x-intercept: –8

y-intercept (x = 0):

72 + 9y = –9(0) → 72 + 9y = 0 → 9y = –72 → y = –8

✔ y-intercept: –8

---

## Problem 4: x + 18 = 9y

Rewrite: x – 9y = –18

x-intercept (y = 0):

x – 9(0) = –18 → x = –18

✔ x-intercept: –18

y-intercept (x = 0):

0 – 9y = –18 → –9y = –18 → y = 2

✔ y-intercept: 2

---

## Problem 5: 42y + 36 = –18x

Rewrite: 18x + 42y = –36

Divide entire equation by 6: 3x + 7y = –6 (optional, but simplifies)

x-intercept (y = 0):

3x + 7(0) = –6 → 3x = –6 → x = –2

✔ x-intercept: –2

y-intercept (x = 0):

3(0) + 7y = –6 → 7y = –6 → y = –6/7

✔ y-intercept: –6/7

---

## Problem 6: 44 + 22x = 11y

Rewrite: 22x – 11y = –44

Divide by 11: 2x – y = –4

x-intercept (y = 0):

2x – 0 = –4 → 2x = –4 → x = –2

✔ x-intercept: –2

y-intercept (x = 0):

2(0) – y = –4 → –y = –4 → y = 4

✔ y-intercept: 4

---

## Problem 7: –90y + 45x = 45

Divide entire equation by 45: –2y + x = 1 → or x – 2y = 1

x-intercept (y = 0):

x – 2(0) = 1 → x = 1

✔ x-intercept: 1

y-intercept (x = 0):

0 – 2y = 1 → –2y = 1 → y = –1/2

✔ y-intercept: –1/2

---

## Problem 8: 24x = 4y – 48

Rewrite: 24x – 4y = –48

Divide by 4: 6x – y = –12

x-intercept (y = 0):

6x – 0 = –12 → 6x = –12 → x = –2

✔ x-intercept: –2

y-intercept (x = 0):

6(0) – y = –12 → –y = –12 → y = 12

✔ y-intercept: 12

---

## Problem 9: 3y = –12x + 9

Divide by 3: y = –4x + 3 ← slope-intercept form!

x-intercept (y = 0):

0 = –12x + 9 → 12x = 9 → x = 9/12 = 3/4

✔ x-intercept: 3/4

y-intercept (x = 0):

3y = –12(0) + 9 → 3y = 9 → y = 3

✔ y-intercept: 3

---

## Problem 10: –10 = –5y + x

Rewrite: x – 5y = –10

x-intercept (y = 0):

x – 0 = –10 → x = –10

✔ x-intercept: –10

y-intercept (x = 0):

0 – 5y = –10 → –5y = –10 → y = 2

✔ y-intercept: 2

---

## ✔ Final Answers:

| Problem | x-intercept | y-intercept |
|---------|-------------|-------------|
| 1 | –2 | 4 |
| 2 | 6 | –2 |
| 3 | –8 | –8 |
| 4 | –18 | 2 |
| 5 | –2 | –6/7 |
| 6 | –2 | 4 |
| 7 | 1 | –1/2 |
| 8 | –2 | 12 |
| 9 | 3/4 | 3 |
| 10 | –10 | 2 |

---

Let me know if you want these plotted or explained in another way!