Find the x- and y-intercepts of the graph of minus, 8, x, plus, 7, y, equals, 40−8*x*+7*y*=40. State each answer as an integer or an improper fraction in simplest form.

To find the x- and y-intercepts of the equation \( -8x + 7y = 40 \), we'll calculate each intercept separately by setting the other variable to zero.

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

\[
-8x + 7(0) = 40
\]

This simplifies to:

\[
-8x = 40
\]

Now, solve for \( x \):

\[
x = \frac{40}{-8} = -5
\]

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

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

\[
-8(0) + 7y = 40
\]

This simplifies to:

\[
7y = 40
\]

Now, solve for \( y \):

\[
y = \frac{40}{7}
\]

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

### Final Answer:
- The x-intercept is \( x = -5 \) (or the point \((-5, 0)\)).
- The y-intercept is \( y = \frac{40}{7} \) (or the point \(\left(0, \frac{40}{7}\right)\)).

Would you like details on how intercepts are used in graphing or have any questions? Here are some related questions to consider:

1. How do you determine the slope of a line from its equation?
2. What is the significance of intercepts in real-world applications?
3. How would you graph the line given the intercepts found?
4. Can the x- and y-intercepts be the same point? If so, under what conditions?
5. What happens if the intercept calculation results in a complex number?

**Tip:** Always check your calculations by substituting the intercepts back into the original equation to ensure accuracy.

Learn how to find the x- and y-intercepts of the linear equation -8x + 7y = 40 with step-by-step solutions and examples. Understand the significance of intercepts in graphing and real-world applications. Suitable for Grades 7-9 students studying linear equations and coordinate geometry.

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