Question

Find the value of r so that the line that passes through each pair of points has the given slope (6,r) (3,3) m=2

Answer 1

$\bf (\stackrel{x_1}{6}~,~\stackrel{y_1}{r})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{r}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{6}}}~~=~~\stackrel{\stackrel{m}{\downarrow }}{2}\implies \cfrac{3-r}{-3}=2\implies 3-r=-6 \\\\\\ -r=-9\implies r=\cfrac{-9}{-1}\implies r=9$