3*x*−8*y*=9    what is x intercept and y intercept

To find the **x-intercept** and **y-intercept** of the equation \( 3x - 8y = 9 \), follow these steps:

### 1. Finding the **x-intercept**:
- The x-intercept occurs when \( y = 0 \).
- Substituting \( y = 0 \) into the equation:
  \[
  3x - 8(0) = 9 \quad \Rightarrow \quad 3x = 9 \quad \Rightarrow \quad x = \frac{9}{3} = 3
  \]
- So, the x-intercept is \( (3, 0) \).

### 2. Finding the **y-intercept**:
- The y-intercept occurs when \( x = 0 \).
- Substituting \( x = 0 \) into the equation:
  \[
  3(0) - 8y = 9 \quad \Rightarrow \quad -8y = 9 \quad \Rightarrow \quad y = \frac{9}{-8} = -\frac{9}{8}
  \]
- So, the y-intercept is \( \left( 0, -\frac{9}{8} \right) \).

### Intercepts:
- **x-intercept**: \( (3, 0) \)
- **y-intercept**: \( \left( 0, -\frac{9}{8} \right) \)

Would you like more details on intercepts or any other clarifications?

Here are some related questions for further exploration:
1. How do you find the slope of the line from the equation \( 3x - 8y = 9 \)?
2. What is the graphical significance of x-intercepts and y-intercepts?
3. How do you convert \( 3x - 8y = 9 \) into slope-intercept form?
4. What happens if you adjust the constants in the equation, e.g., changing 9 to 12?
5. Can there be cases where an equation has no x-intercept or y-intercept?

**Tip**: To easily find intercepts, remember that setting one variable to 0 gives you the intercept for the other.

3*x - 8*y = 9    what is x intercept and y intercept

Learn how to find the x-intercept and y-intercept of the linear equation 3x - 8y = 9. This problem demonstrates key algebraic concepts such as intercepts and solving linear equations. Step-by-step explanation suitable for Grades 8-10.

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