Question

find the x-intercept and y-intercept of the graph of the equation $6x + 2y = 8$.

a) x-intercept: 6
y-intercept: 2

b) x-intercept: $\frac{3}{4}$
y-intercept: 4

c) x-intercept: $1\frac{1}{3}$
y-intercept: 4

d) x-intercept: 4
y-intercept: $1\frac{1}{3}$

Explanation:

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

Substitute \( y = 0 \) into \( 6x + 2y = 8 \):
\( 6x + 2(0) = 8 \)
Simplify: \( 6x = 8 \)
Solve for \( x \): \( x = \frac{8}{6} = \frac{4}{3} = 1\frac{1}{3} \)

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

Substitute \( x = 0 \) into \( 6x + 2y = 8 \):
\( 6(0) + 2y = 8 \)
Simplify: \( 2y = 8 \)
Solve for \( y \): \( y = \frac{8}{2} = 4 \)

Answer:

C) x-intercept: \( 1\frac{1}{3} \), y-intercept: 4