https://file.aiquickdraw.com/mathbot/file/1727229270819uiyqnyaq.jpg

The equation given in the image is:

\[
4x - 5y = -6
\]

We need to find the **x-intercept** and the **y-intercept**.

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

\[
4x - 5(0) = -6 \implies 4x = -6 \implies x = \frac{-6}{4} = \frac{-3}{2}
\]

Thus, the **x-intercept** is \( \left( -\frac{3}{2}, 0 \right) \).

### 2. **Finding the y-intercept:**
The y-intercept occurs when \( x = 0 \). Substituting \( x = 0 \) in the equation:

\[
4(0) - 5y = -6 \implies -5y = -6 \implies y = \frac{-6}{-5} = \frac{6}{5}
\]

Thus, the **y-intercept** is \( \left( 0, \frac{6}{5} \right) \).

### Conclusion:
- x-intercept: \( \left( -\frac{3}{2}, 0 \right) \)
- y-intercept: \( \left( 0, \frac{6}{5} \right) \)

The correct intercepts are \( (-\frac{3}{2}, 0) \) for x and \( (0, \frac{6}{5}) \) for y. However, in the image, the y-intercept is incorrectly stated as \( \left( \frac{6}{5}, 0 \right) \), which seems to be a mistake in the question.

Would you like more details or have any questions about this? 

Here are 5 related questions:
1. How do you find intercepts for nonlinear equations?
2. Can a line have more than one x- or y-intercept?
3. How do intercepts help in graphing a linear equation?
4. What is the significance of slope in relation to intercepts?
5. How do we convert equations to slope-intercept form?

**Tip**: Always check your intercepts by plugging them back into the original equation to ensure correctness!

Find the x-intercept and y-intercept of the line 4x - 5y = -6.

Learn how to find the x- and y-intercepts of the linear equation 4x - 5y = -6. Step-by-step solution, applying algebraic concepts to calculate the intercepts: (-3/2, 0) for x and (0, 6/5) for y. Suitable for students in Grades 8-10.

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