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To find the x- and y-intercepts of the equation:

\[
-8x + 7y = 40
\]

we'll solve for each intercept by setting the other variable to zero.

### Finding the x-intercept:
The x-intercept occurs where \( y = 0 \).

1. Substitute \( y = 0 \) into the equation:
   \[
   -8x + 7(0) = 40
   \]
   \[
   -8x = 40
   \]

2. Solve for \( x \):
   \[
   x = \frac{40}{-8} = -5
   \]

So, the x-intercept is \((-5, 0)\).

### Finding the y-intercept:
The y-intercept occurs where \( x = 0 \).

1. Substitute \( x = 0 \) into the equation:
   \[
   -8(0) + 7y = 40
   \]
   \[
   7y = 40
   \]

2. Solve for \( y \):
   \[
   y = \frac{40}{7}
   \]

So, the y-intercept is \(\left(0, \frac{40}{7}\right)\).

### Final Answer:
- **x-intercept**: \(-5\)
- **y-intercept**: \(\frac{40}{7}\)

Would you like more details on intercepts or have any further questions?

Here are some related questions to expand your understanding:
1. How do you find the slope of a line given in standard form, such as \(-8x + 7y = 40\)?
2. What is the process to convert an equation in standard form to slope-intercept form?
3. Can you find the distance between the x- and y-intercepts of this line?
4. How does the standard form of a line help identify intercepts?
5. What would the intercepts be if the constant term on the right side of the equation was changed?

**Tip:** To quickly find intercepts, remember that setting \( y = 0 \) finds the x-intercept and setting \( x = 0 \) finds the y-intercept.

Find the x- and y-intercepts of the graph of -8x + 7y = 40. 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 -8x + 7y = 40. This solution provides step-by-step calculations to solve for each intercept in simplest form. Ideal for students in Grades 8-10 studying linear equations and intercepts.

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