Question

The points (3,-10) and (7,r) lie on a line with slope 5/4. Find the missing coordinate r.

Answer 1

$(\stackrel{x_1}{3}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{r}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{r}-\stackrel{y1}{(-10)}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{3}}} \implies \cfrac{r +10}{4}~~ = ~~\stackrel{\stackrel{m}{\downarrow }}{\cfrac{5}{4}} \\\\\\ 4r+40=20\implies 4r=-20\implies r=\cfrac{-20}{4}\implies {\Large \begin{array}{llll} r=-5 \end{array}}$