Question

What is the slope of the line that passes through the points (−4,0) and (2, 0)? Write your answer in simplest form.

Answer 1

You can see that both points sit on the x axis, which means that the line passing trough them is actually the x axis, which is in particular a horizontal line.

Every horizontal line has slope 0, so this is the case for this line.

If you didn't realize this and want to use the "rise over run" formula anyway, you'd obviously come to the same result:

$m = \dfrac{\Delta y}{\Delta x} = \dfrac{0-0}{-4-2} = \dfrac{0}{-6} = 0$

Answer 2

since both points have a y- coordinate of zero, this is a horizontal line parallel to the x- axis

hence slope = 0