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To find the **x-intercept** and **y-intercept** of the given line:

\[
-8x + 5y = 14
\]

We need to follow these steps:

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

\[
-8x + 5(0) = 14 \implies -8x = 14
\]

Solving for \( x \):

\[
x = \frac{14}{-8} = -\frac{7}{4}
\]

So, the **x-intercept** is \( x = -\frac{7}{4} \).

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

\[
-8(0) + 5y = 14 \implies 5y = 14
\]

Solving for \( y \):

\[
y = \frac{14}{5}
\]

So, the **y-intercept** is \( y = \frac{14}{5} \).

### Final Answer:
- The **x-intercept** is \( -\frac{7}{4} \).
- The **y-intercept** is \( \frac{14}{5} \).

Do you have any questions or would you like more details on how this was solved?

Here are some related questions to expand on this topic:
1. How do we graph a line using intercepts?
2. What is the slope of the line given by the equation \( -8x + 5y = 14 \)?
3. How do you rewrite the equation in slope-intercept form?
4. What are the steps to find intercepts for quadratic equations?
5. How do the intercepts help in understanding the behavior of a linear function?

**Tip**: The x-intercept occurs where the graph crosses the x-axis, and the y-intercept occurs where the graph crosses the y-axis.

Find the x-intercept and y-intercept of the line -8x + 5y = 14. Write your answers as exact values. Do not write your answers as ordered pairs.

Learn how to find the x-intercept and y-intercept of the linear equation -8x + 5y = 14. This problem covers key algebraic concepts, suitable for students in Grades 7-9. The x-intercept occurs at x = -7/4, and the y-intercept occurs at y = 14/5.

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