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To find the **x-intercept** and **y-intercept** of the line given by the equation \( 7x - 5y = -8 \), follow these steps:

### (a) **y-intercept**:
The y-intercept occurs when \( x = 0 \). We can find it by substituting \( x = 0 \) into the equation and solving for \( y \).

\[
7(0) - 5y = -8
\]
\[
-5y = -8
\]
\[
y = \frac{-8}{-5} = \frac{8}{5}
\]

Thus, the **y-intercept** is \( \left( 0, \frac{8}{5} \right) \).

### (b) **x-intercept**:
The x-intercept occurs when \( y = 0 \). We can find it by substituting \( y = 0 \) into the equation and solving for \( x \).

\[
7x - 5(0) = -8
\]
\[
7x = -8
\]
\[
x = \frac{-8}{7}
\]

Thus, the **x-intercept** is \( \left( \frac{-8}{7}, 0 \right) \).

### Final Answer:
- **y-intercept**: \( \left( 0, \frac{8}{5} \right) \)
- **x-intercept**: \( \left( \frac{-8}{7}, 0 \right) \)

Would you like any further explanation on how to find intercepts or how to rewrite the equation in slope-intercept form?

### Related Questions:
1. How do you convert this equation into slope-intercept form?
2. How can you find the slope from the given equation?
3. How do intercepts help in graphing the line?
4. What is the importance of intercepts in real-life applications?
5. How do you find intercepts for quadratic equations?

#### Tip:
To find intercepts, set one variable to zero and solve for the other. This is a simple way to identify where the line crosses the x- and y-axes.

Find the y-intercept and x-intercept of the line 7x - 5y = -8.

Explore how to find the x-intercept and y-intercept of the line 7x - 5y = -8 with step-by-step calculations. Learn the concepts behind linear equations, intercepts, and how they relate to graphing. Perfect for students in Grades 7-9.

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