r = -6
Step-by-step explanation:
The slope of a line is defined as
[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
Let [tex]P_1(-4, 2)[/tex] and [tex]P_2(4, r)[/tex]. Since m = -1, we can write
[tex]-1 = \dfrac{r - 2}{4 - (-4)} \Rightarrow -1 = \dfrac{r - 2}{8}[/tex]
or
[tex]r - 2 = -8 \Rightarrow r = -6[/tex]
