Question

find the x-intercept.
$y = \frac{6x - 12}{2x + 12}$
$(?, 0)$

Explanation:

Step1: Recall x-intercept definition

The x-intercept occurs where \( y = 0 \). So set \( y = 0 \) in the equation \( y=\frac{6x - 12}{2x + 12} \).

Step2: Solve for x

Set \( 0=\frac{6x - 12}{2x + 12} \). A fraction equals zero when the numerator is zero (and denominator not zero). So solve \( 6x - 12 = 0 \).
Add 12 to both sides: \( 6x=12 \).
Divide by 6: \( x = 2 \).
Check denominator: \( 2(2)+12 = 16
eq0 \), so valid.

Answer:

\( 2 \)