Finding x and y intercepts worksheet: Fill out & sign online | DocHub - Free Printable

Let's solve each problem step by step to find the x-intercept and y-intercept of each line.

---

🔹 How to Find Intercepts:

- x-intercept: Set $ y = 0 $, then solve for $ x $.
This gives the point where the line crosses the x-axis.

- y-intercept: Set $ x = 0 $, then solve for $ y $.
This gives the point where the line crosses the y-axis.

---

We’ll go through each equation:

---

1. $ 4y = 3x - 2 $

#### x-intercept (set $ y = 0 $):
$$
4(0) = 3x - 2 \Rightarrow 0 = 3x - 2 \Rightarrow 3x = 2 \Rightarrow x = \frac{2}{3}
$$
✔ x-intercept: $ \left(\frac{2}{3}, 0\right) $

#### y-intercept (set $ x = 0 $):
$$
4y = 3(0) - 2 \Rightarrow 4y = -2 \Rightarrow y = -\frac{1}{2}
$$
✔ y-intercept: $ \left(0, -\frac{1}{2}\right) $

---

2. $ 5y = x + 6 $

#### x-intercept ($ y = 0 $):
$$
5(0) = x + 6 \Rightarrow 0 = x + 6 \Rightarrow x = -6
$$
✔ x-intercept: $ (-6, 0) $

#### y-intercept ($ x = 0 $):
$$
5y = 0 + 6 \Rightarrow 5y = 6 \Rightarrow y = \frac{6}{5}
$$
✔ y-intercept: $ \left(0, \frac{6}{5}\right) $

---

3. $ y = 7x + 3 $

#### x-intercept ($ y = 0 $):
$$
0 = 7x + 3 \Rightarrow 7x = -3 \Rightarrow x = -\frac{3}{7}
$$
✔ x-intercept: $ \left(-\frac{3}{7}, 0\right) $

#### y-intercept ($ x = 0 $):
$$
y = 7(0) + 3 = 3
$$
✔ y-intercept: $ (0, 3) $

---

4. $ 8y = 2x + 10 $

#### x-intercept ($ y = 0 $):
$$
8(0) = 2x + 10 \Rightarrow 0 = 2x + 10 \Rightarrow 2x = -10 \Rightarrow x = -5
$$
✔ x-intercept: $ (-5, 0) $

#### y-intercept ($ x = 0 $):
$$
8y = 2(0) + 10 \Rightarrow 8y = 10 \Rightarrow y = \frac{10}{8} = \frac{5}{4}
$$
✔ y-intercept: $ \left(0, \frac{5}{4}\right) $

---

5. $ 5y = 7x - 3 $

#### x-intercept ($ y = 0 $):
$$
5(0) = 7x - 3 \Rightarrow 0 = 7x - 3 \Rightarrow 7x = 3 \Rightarrow x = \frac{3}{7}
$$
✔ x-intercept: $ \left(\frac{3}{7}, 0\right) $

#### y-intercept ($ x = 0 $):
$$
5y = 7(0) - 3 \Rightarrow 5y = -3 \Rightarrow y = -\frac{3}{5}
$$
✔ y-intercept: $ \left(0, -\frac{3}{5}\right) $

---

6. $ 9y = 4x - 6 $

#### x-intercept ($ y = 0 $):
$$
9(0) = 4x - 6 \Rightarrow 0 = 4x - 6 \Rightarrow 4x = 6 \Rightarrow x = \frac{3}{2}
$$
✔ x-intercept: $ \left(\frac{3}{2}, 0\right) $

#### y-intercept ($ x = 0 $):
$$
9y = 4(0) - 6 \Rightarrow 9y = -6 \Rightarrow y = -\frac{2}{3}
$$
✔ y-intercept: $ \left(0, -\frac{2}{3}\right) $

---

7. $ 8y = 3x - 9 $

#### x-intercept ($ y = 0 $):
$$
8(0) = 3x - 9 \Rightarrow 0 = 3x - 9 \Rightarrow 3x = 9 \Rightarrow x = 3
$$
✔ x-intercept: $ (3, 0) $

#### y-intercept ($ x = 0 $):
$$
8y = 3(0) - 9 \Rightarrow 8y = -9 \Rightarrow y = -\frac{9}{8}
$$
✔ y-intercept: $ \left(0, -\frac{9}{8}\right) $

---

8. $ y = 3x - 8 $

#### x-intercept ($ y = 0 $):
$$
0 = 3x - 8 \Rightarrow 3x = 8 \Rightarrow x = \frac{8}{3}
$$
✔ x-intercept: $ \left(\frac{8}{3}, 0\right) $

#### y-intercept ($ x = 0 $):
$$
y = 3(0) - 8 = -8
$$
✔ y-intercept: $ (0, -8) $

---

9. $ y = x - 14 $

#### x-intercept ($ y = 0 $):
$$
0 = x - 14 \Rightarrow x = 14
$$
✔ x-intercept: $ (14, 0) $

#### y-intercept ($ x = 0 $):
$$
y = 0 - 14 = -14
$$
✔ y-intercept: $ (0, -14) $

---

10. $ 7y = x + 12 $

#### x-intercept ($ y = 0 $):
$$
7(0) = x + 12 \Rightarrow 0 = x + 12 \Rightarrow x = -12
$$
✔ x-intercept: $ (-12, 0) $

#### y-intercept ($ x = 0 $):
$$
7y = 0 + 12 \Rightarrow 7y = 12 \Rightarrow y = \frac{12}{7}
$$
✔ y-intercept: $ \left(0, \frac{12}{7}\right) $

---

✔ Final Answers Summary:

| Problem | x-intercept | y-intercept |
|--------|-------------|-------------|
| 1 | $ \left(\frac{2}{3}, 0\right) $ | $ \left(0, -\frac{1}{2}\right) $ |
| 2 | $ (-6, 0) $ | $ \left(0, \frac{6}{5}\right) $ |
| 3 | $ \left(-\frac{3}{7}, 0\right) $ | $ (0, 3) $ |
| 4 | $ (-5, 0) $ | $ \left(0, \frac{5}{4}\right) $ |
| 5 | $ \left(\frac{3}{7}, 0\right) $ | $ \left(0, -\frac{3}{5}\right) $ |
| 6 | $ \left(\frac{3}{2}, 0\right) $ | $ \left(0, -\frac{2}{3}\right) $ |
| 7 | $ (3, 0) $ | $ \left(0, -\frac{9}{8}\right) $ |
| 8 | $ \left(\frac{8}{3}, 0\right) $ | $ (0, -8) $ |
| 9 | $ (14, 0) $ | $ (0, -14) $ |
| 10 | $ (-12, 0) $ | $ \left(0, \frac{12}{7}\right) $ |

---

Let me know if you'd like this formatted as a printable answer key!