y=3x-9 find the x and y intercepts of the line

The equation of the line is \( y = 3x - 9 \). To find the intercepts, follow these steps:

### 1. **Finding the y-intercept:**
The y-intercept is where the line crosses the y-axis, which occurs when \( x = 0 \).

- Substitute \( x = 0 \) into the equation:
  \[
  y = 3(0) - 9 = -9
  \]
  So, the y-intercept is \( (0, -9) \).

### 2. **Finding the x-intercept:**
The x-intercept is where the line crosses the x-axis, which occurs when \( y = 0 \).

- Set \( y = 0 \) in the equation:
  \[
  0 = 3x - 9
  \]
  - Add 9 to both sides:
    \[
    9 = 3x
    \]
  - Divide by 3:
    \[
    x = 3
    \]
  So, the x-intercept is \( (3, 0) \).

### Summary:
- The y-intercept is \( (0, -9) \).
- The x-intercept is \( (3, 0) \).

Would you like more details or have any questions?

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Here are 5 related questions:
1. What does the slope of this line represent geometrically?
2. How would the intercepts change if the equation was \( y = 3x + 9 \)?
3. What is the slope of a line parallel to \( y = 3x - 9 \)?
4. How do we find the x-intercept in a quadratic equation?
5. Can a line have more than one x-intercept?

**Tip:** The x-intercept occurs where the line crosses the x-axis, so the y-value is always 0 at that point.

Discover how to find the x and y intercepts of the line y=3x-9 with a clear step-by-step guide. This solution explores key linear equation concepts and demonstrates how to calculate intercepts. Perfect for students in Grades 8-10.

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