Question

find the x-intercept.
$y = \frac{3x + 27}{x - 9}$
$(?, 0)$

Explanation:

Step1: Recall x-intercept definition

The x - intercept of a function is the point where \(y = 0\). So we set \(y=0\) in the equation \(y=\frac{3x + 27}{x - 9}\).

Step2: Solve for x

Set \(0=\frac{3x + 27}{x - 9}\). Since a fraction is zero when its numerator is zero (and the denominator is not zero), we solve \(3x+27 = 0\) (and check \(x-9
eq0\) later).
Subtract 27 from both sides: \(3x=- 27\).
Divide both sides by 3: \(x=-9\).
Now check the denominator: when \(x = - 9\), \(x-9=-9 - 9=-18
eq0\), so \(x=-9\) is valid.

Answer:

\(-9\)