Question

The points (-10, r) and (-6, 4) lle on a line with slope

3
4
.
Find the missing coordinate r.

Answer 1

`(\stackrel{x_1}{-10}~,~\stackrel{y_1}{r})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{r}}}{\underset{run} {\underset{x_2}{-6}-\underset{x_1}{(-10)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{\cfrac{3}{4}}\implies \cfrac{4-r}{-6+10}=\cfrac{3}{4}\implies \cfrac{4-r}{4}=\cfrac{3}{4} \\\\\\ 4-r=3\implies 4=3+r\implies 1=r`