Question

The points (-1 14) and (2 r) lie on a line with slope -2. Find the missing coordinate r.

Answer 1

`(\stackrel{x_1}{-1}~,~\stackrel{y_1}{14})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{r}) \hspace{5em} \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{r}-\stackrel{y1}{14}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{-2} \\\\\\ \cfrac{r-14}{2+1}=-2\implies \cfrac{r-14}{3}=-2\implies r-14=-6\implies r=8`