https://file.aiquickdraw.com/mathbot/file/1726617436212moad1xfk.jpg

Let's solve the problem shown in the image. 

We are given the equation of the line:  
\[
2x - 5y = 6
\]
We need to find the **x-intercept** and the **y-intercept**.

### 1. Finding the **x-intercept**:
To find the x-intercept, set \( y = 0 \) in the equation and solve for \( x \).

\[
2x - 5(0) = 6
\]
\[
2x = 6
\]
\[
x = \frac{6}{2} = 3
\]

Thus, the **x-intercept** is \( x = 3 \).

### 2. Finding the **y-intercept**:
To find the y-intercept, set \( x = 0 \) in the equation and solve for \( y \).

\[
2(0) - 5y = 6
\]
\[
-5y = 6
\]
\[
y = \frac{6}{-5} = -\frac{6}{5}
\]

Thus, the **y-intercept** is \( y = -\frac{6}{5} \).

### Final Answer:
- **x-intercept**: \( 3 \)
- **y-intercept**: \( -\frac{6}{5} \)

You can now enter these values into the fields provided.

Would you like more details or have any questions? Here are some related questions to deepen your understanding:

1. How do you find the slope of the line from the equation \( 2x - 5y = 6 \)?
2. What is the significance of intercepts in the graph of a line?
3. Can you convert the equation \( 2x - 5y = 6 \) into slope-intercept form?
4. What happens if both the x- and y-intercepts are negative?
5. How would you graph the line given by \( 2x - 5y = 6 \) using the intercepts?

**Tip**: Always set the opposite variable to zero when finding intercepts.

Find the x- and y-intercepts of the graph of 2x - 5y = 6. State each answer as an integer or an improper fraction in simplest form.

Learn how to find the x- and y-intercepts of the linear equation 2x - 5y = 6. This solution explains how to calculate intercepts by setting the opposite variable to zero, providing a detailed step-by-step process. Suitable for students in Grades 8-10.

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