Question

The points (-5,13) and (-2,r) lie on a line with slope -3. Find the missing coordinate r.

Answer 1

`(\stackrel{x_1}{-5}~,~\stackrel{y_1}{13})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{r}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{r}-\stackrel{y1}{13}}}{\underset{\textit{\large run}} {\underset{x_2}{-2}-\underset{x_1}{(-5)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ -3 }\implies \cfrac{r-13}{-2+5}=-3\implies \cfrac{r-13}{3}=-3 \\\\\\ r-13=-9\implies r=4`