Question

find the x- and y-intercepts of the graph of $-6x + 4y = 40$. state each answer as an integer or an improper fraction in simplest form.

answer

x-intercept: \boxed{} y-intercept: \boxed{}

Explanation:

Step1: Find x-intercept (set y=0)

Set \( y = 0 \) in \( -6x + 4y = 40 \):
\( -6x + 4(0) = 40 \)
Simplify: \( -6x = 40 \)
Solve for \( x \): \( x = \frac{40}{-6} = -\frac{20}{3} \)

Step2: Find y-intercept (set x=0)

Set \( x = 0 \) in \( -6x + 4y = 40 \):
\( -6(0) + 4y = 40 \)
Simplify: \( 4y = 40 \)
Solve for \( y \): \( y = \frac{40}{4} = 10 \)

Answer:

x-intercept: \(-\frac{20}{3}\)
y-intercept: \(10\)