Question

Solve for a if the line through the two given points has the given slope.

(3, – 4a) and (1, a), m = - 5
a = ?

Answer 1

`(\stackrel{x_1}{3}~,~\stackrel{y_1}{-4a})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{a}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{a}-\stackrel{y1}{(-4a)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{3}}}~~=~~\stackrel{\stackrel{m}{\downarrow }}{-5} \\\\\\ \cfrac{a+4a}{-2}=-5\implies \cfrac{5a}{-2}=-5\implies 5a=10\implies a=\cfrac{10}{5}\implies a=2`