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To determine the intercepts of the line \( y = 10x - 32 \), we will follow these steps:

### 1. **Y-intercept:**
The y-intercept occurs when \( x = 0 \).

- Substitute \( x = 0 \) into the equation:
  \[
  y = 10(0) - 32 = -32
  \]
- So, the y-intercept is \( (0, -32) \).

### 2. **X-intercept:**
The x-intercept occurs when \( y = 0 \).

- Set \( y = 0 \) and solve for \( x \):
  \[
  0 = 10x - 32
  \]
  \[
  10x = 32
  \]
  \[
  x = \frac{32}{10} = \frac{16}{5}
  \]
- So, the x-intercept is \( \left( \frac{16}{5}, 0 \right) \).

### Final Answer:
- **Y-intercept**: \( (0, -32) \)
- **X-intercept**: \( \left( \frac{16}{5}, 0 \right) \)

Do you want more details or have any questions? 

Here are 5 related questions:
1. How do you find the slope of the line from the equation?
2. What does the y-intercept represent graphically?
3. How can you graph the line using the intercepts?
4. Can you convert this linear equation to slope-intercept form?
5. How would the intercepts change if the slope or constant term were altered?

**Tip**: When finding intercepts, setting one variable to 0 and solving for the other is the key technique.

Determine the intercepts of the line y = 10x - 32. Do not round your answers.

Learn how to find the x- and y-intercepts of the line represented by y = 10x - 32. This step-by-step guide covers linear equations and finding intercepts, suitable for Grades 7-9.

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