Question

find the x-intercept and y-intercept of the line.
-6x + 4y = 21
write your answers as exact values. do not write your answers as ordered pairs.
x -intercept:
y -intercept:

Explanation:

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

Set \( y = 0 \) in the equation \( -6x + 4y = 21 \). Then we have \( -6x + 4(0) = 21 \), which simplifies to \( -6x = 21 \). Solving for \( x \), we divide both sides by -6: \( x = \frac{21}{-6} = -\frac{7}{2} \).

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

Set \( x = 0 \) in the equation \( -6x + 4y = 21 \). Then we have \( -6(0) + 4y = 21 \), which simplifies to \( 4y = 21 \). Solving for \( y \), we divide both sides by 4: \( y = \frac{21}{4} \).

Answer:

x-intercept: \(-\frac{7}{2}\)
y-intercept: \(\frac{21}{4}\)