https://file.aiquickdraw.com/mathbot/file/1729505380039kt47hgcc.jpg

Let's solve each equation to find the **x-intercepts** and **y-intercepts**.

### 37. \( x - y = 5 \)

- **x-intercept**: Set \( y = 0 \).
  \[
  x - 0 = 5 \quad \Rightarrow \quad x = 5
  \]
  So, the x-intercept is \( (5, 0) \).

- **y-intercept**: Set \( x = 0 \).
  \[
  0 - y = 5 \quad \Rightarrow \quad y = -5
  \]
  So, the y-intercept is \( (0, -5) \).

---

### 38. \( x - y = -4 \)

- **x-intercept**: Set \( y = 0 \).
  \[
  x - 0 = -4 \quad \Rightarrow \quad x = -4
  \]
  So, the x-intercept is \( (-4, 0) \).

- **y-intercept**: Set \( x = 0 \).
  \[
  0 - y = -4 \quad \Rightarrow \quad y = 4
  \]
  So, the y-intercept is \( (0, 4) \).

---

### 39. \( 3x + y = 6 \)

- **x-intercept**: Set \( y = 0 \).
  \[
  3x + 0 = 6 \quad \Rightarrow \quad x = 2
  \]
  So, the x-intercept is \( (2, 0) \).

- **y-intercept**: Set \( x = 0 \).
  \[
  3(0) + y = 6 \quad \Rightarrow \quad y = 6
  \]
  So, the y-intercept is \( (0, 6) \).

---

### 40. \( x - 2y = 8 \)

- **x-intercept**: Set \( y = 0 \).
  \[
  x - 2(0) = 8 \quad \Rightarrow \quad x = 8
  \]
  So, the x-intercept is \( (8, 0) \).

- **y-intercept**: Set \( x = 0 \).
  \[
  0 - 2y = 8 \quad \Rightarrow \quad y = -4
  \]
  So, the y-intercept is \( (0, -4) \).

---

### 41. \( 4x - y = 8 \)

- **x-intercept**: Set \( y = 0 \).
  \[
  4x - 0 = 8 \quad \Rightarrow \quad x = 2
  \]
  So, the x-intercept is \( (2, 0) \).

- **y-intercept**: Set \( x = 0 \).
  \[
  4(0) - y = 8 \quad \Rightarrow \quad y = -8
  \]
  So, the y-intercept is \( (0, -8) \).

---

### 42. \( 5x - y = 5 \)

- **x-intercept**: Set \( y = 0 \).
  \[
  5x - 0 = 5 \quad \Rightarrow \quad x = 1
  \]
  So, the x-intercept is \( (1, 0) \).

- **y-intercept**: Set \( x = 0 \).
  \[
  5(0) - y = 5 \quad \Rightarrow \quad y = -5
  \]
  So, the y-intercept is \( (0, -5) \).

---

### 43. \( 2x + 5y = 10 \)

- **x-intercept**: Set \( y = 0 \).
  \[
  2x + 5(0) = 10 \quad \Rightarrow \quad x = 5
  \]
  So, the x-intercept is \( (5, 0) \).

- **y-intercept**: Set \( x = 0 \).
  \[
  2(0) + 5y = 10 \quad \Rightarrow \quad y = 2
  \]
  So, the y-intercept is \( (0, 2) \).

---

### 44. \( 3x - 2y = 12 \)

- **x-intercept**: Set \( y = 0 \).
  \[
  3x - 2(0) = 12 \quad \Rightarrow \quad x = 4
  \]
  So, the x-intercept is \( (4, 0) \).

- **y-intercept**: Set \( x = 0 \).
  \[
  3(0) - 2y = 12 \quad \Rightarrow \quad y = -6
  \]
  So, the y-intercept is \( (0, -6) \).

---

Would you like any more details on these solutions or have further questions?

### Follow-up questions:
1. How do you find the slope of a linear equation from intercepts?
2. How do x- and y-intercepts help in graphing a line?
3. What is the general form of a linear equation, and how do you convert it to slope-intercept form?
4. Can you use the intercepts to check the accuracy of the solution graphically?
5. What happens when an equation has no x-intercept or no y-intercept?

**Tip:** Always double-check your intercepts by substituting them back into the original equation to verify!

In the following exercises, find the intercepts for each equation: 37. x - y = 5, 38. x - y = -4, 39. 3x + y = 6, 40. x - 2y = 8, 41. 4x - y = 8, 42. 5x - y = 5, 43. 2x + 5y = 10, 44. 3x - 2y = 12.

Learn how to find the x- and y-intercepts for linear equations such as x - y = 5 and 3x + y = 6. Follow a step-by-step guide on setting y or x to 0 to solve for the corresponding intercepts. Suitable for students in Grades 8-10.

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