Question

The points (-1,9) and (4, r) lie on a line with slope -3 find the missing coordinate r

r=?

Answer 1

`(\stackrel{x_1}{-1}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{r}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{r}-\stackrel{y1}{9}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{(-1)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ -3 }\implies \cfrac{r-9}{4+1}=-3\implies \cfrac{r-9}{5}=-3 \\\\\\ r-9=-15\implies \boxed{r=-6}`