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.