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To find the intercepts of the line given by the equation \( y = -3x + 12 \), we'll calculate both the **y-intercept** and the **x-intercept**.

### Step 1: Finding the y-intercept
The **y-intercept** occurs where \( x = 0 \). Substituting \( x = 0 \) into the equation:

\[
y = -3(0) + 12 = 12
\]

So, the y-intercept is \( (0, 12) \).

### Step 2: Finding the x-intercept
The **x-intercept** occurs where \( y = 0 \). Set \( y = 0 \) in the equation and solve for \( x \):

\[
0 = -3x + 12
\]

Solve for \( x \):

\[
3x = 12 \quad \Rightarrow \quad x = \frac{12}{3} = 4
\]

So, the x-intercept is \( (4, 0) \).

### Final Answer:
- **y-intercept**: \( (0, 12) \)
- **x-intercept**: \( (4, 0) \)

Let me know if you'd like any further details or clarifications!

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Here are 5 related questions to expand on this topic:
1. How do you find the slope of the line from the equation \( y = -3x + 12 \)?
2. What does the slope of \( -3 \) indicate about the direction of the line?
3. Can you write the equation of the line in point-slope form using the intercepts?
4. How would the intercepts change if the equation were \( y = 2x - 8 \)?
5. What would the graph of the equation \( y = -3x + 12 \) look like?

**Tip**: The x-intercept is found by setting \( y = 0 \), and the y-intercept is found by setting \( x = 0 \)—use this for any linear equation!

Determine the intercepts of the line y = -3x + 12. Do not round your answers.

Learn how to determine the intercepts of the line y = -3x + 12 by calculating the x-intercept and y-intercept. This problem covers essential concepts in linear equations and coordinate geometry, suitable for students in Grades 8-10.

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