To find the x-intercept of the given function [tex]\( y = \frac{3x + 12}{x - 6} \)[/tex], we need to determine the value of [tex]\( x \)[/tex] where [tex]\( y \)[/tex] equals zero. Follow these steps:
1. Set the function equal to zero to find the x-intercept:
[tex]\[
0 = \frac{3x + 12}{x - 6}
\][/tex]
2. For a fraction to be zero, the numerator must be zero, while the denominator is not zero. Therefore, we set the numerator equal to zero:
[tex]\[
3x + 12 = 0
\][/tex]
3. Solve the equation [tex]\( 3x + 12 = 0 \)[/tex] for [tex]\( x \)[/tex]:
- Subtract 12 from both sides:
[tex]\[
3x = -12
\][/tex]
- Divide both sides by 3:
[tex]\[
x = -4
\][/tex]
So, the x-intercept of the function [tex]\( y = \frac{3x + 12}{x - 6} \)[/tex] is [tex]\( x = -4 \)[/tex].
Thus, the x-intercept is:
[tex]\[
(-4, 0)
\][/tex]
