Answer
The x-intercept is $9$
Work Step by Step
We must find the equation of the line first. We can use this template to find the equation of the line, where the slope is $m$ and the y-intercept is $b$
$y = mx + b$
To find the slope, we need to use the formula
$m = \frac{y_2-y_1}{x_2-x_1}$
Plug in the points $(-2,11)$ and $(6,3)$
$m = \frac{3-11}{6-(-2)}$
$m = -8/8$
$ m = -1$
Now, fill in the newly acquired information into the template equation
$y = -x +b$
Now, plug in $(6,3)$ (or any other point) to find $b$
$3 =-6 + b$
$9 = b$
$b = 9$
Fill in the newly acquired information.
$y = -x + 9$
We have the equation. To find the x-intercept, plug in $y = 0$
$0 = -x + 9$
$x = 9$
The x-intercept is $9$
