Question

find the x-intercept and y-intercept of the line.
-2x + 3y = 8
x -intercept:

y -intercept:

Explanation:

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

Set \( y = 0 \) in the equation \( -2x + 3y = 8 \).
We get \( -2x + 3(0) = 8 \), which simplifies to \( -2x = 8 \).
Divide both sides by -2: \( x = \frac{8}{-2} = -4 \).

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

Set \( x = 0 \) in the equation \( -2x + 3y = 8 \).
We get \( -2(0) + 3y = 8 \), which simplifies to \( 3y = 8 \).
Divide both sides by 3: \( y = \frac{8}{3} \).

Answer:

x-intercept: \(-4\)
y-intercept: \(\frac{8}{3}\)