Question

A line that includes the points (– 6,9) and (– 9,a) has a slope of 4. What is the value of a

Answer 1

`(\stackrel{x_1}{-6}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{-9}~,~\stackrel{y_2}{a}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{a}-\stackrel{y1}{9}}}{\underset{run} {\underset{x_2}{-9}-\underset{x_1}{(-6)}}} \implies \cfrac{a -9}{-9 +6}~~ = ~~\stackrel{\stackrel{m}{\downarrow }}{4}\implies \cfrac{a-9}{-3}=4 \\\\\\ a-9=-12\implies \boxed{a=-3}`