To find the **x-intercept** of the equation \( 2x + 5y = 9 \), we set \( y = 0 \) because the x-intercept occurs when the graph crosses the x-axis, and at that point, the value of \( y \) is always 0.

### Steps:
1. Set \( y = 0 \) in the equation:
   \[
   2x + 5(0) = 9
   \]
   \[
   2x = 9
   \]

2. Solve for \( x \):
   \[
   x = \frac{9}{2}
   \]
   \[
   x = 4.5
   \]

### Conclusion:
The **x-intercept** is at \( x = 4.5 \). So, the x-intercept is \( (4.5, 0) \).

Would you like more details on any part of the solution? 

Here are some related questions to explore:
1. What is the y-intercept of the equation?
2. How would the graph of the equation look?
3. Can this equation be written in slope-intercept form?
4. How do we solve for \( y \) in terms of \( x \)?
5. What does the slope represent in this equation?

**Tip:** The x-intercept is where the graph touches the x-axis, so always substitute \( y = 0 \) to find it.

Discover how to find the x-intercept of the linear equation 2x + 5y = 9 with this step-by-step solution. This algebraic problem highlights key concepts like linear equations and intercepts, making it perfect for students in Grades 8-10.

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