Question

The points (4,r) and (8,-5) lie on a line with slope -1. Find the missing coordinate rp

Answer 1

`\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{r})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-5-r}{8-4}~~=~~\stackrel{\stackrel{m}{\downarrow }}{-1}\implies \cfrac{-5-r}{4}=-1 \\\\\\ -5-r=-4\implies -r=1\implies r=-1`