Question

a line that includes the points (5,r) and (-2,13) has a slope of -1. what is the value of r?

Answer 1

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have (5, r), (-2, 13) and m = -1.

Substitute:

$\dfrac{13-r}{-2-5}=-1\\\\\dfrac{13-r}{-7}=-1\qquad|\cdot(-7)\\\\13-r=7\qquad|-13\\\\-r=-6\to\boxed{r=6}$