Question

A straight line has slope 1 and goes through the points (0, -1) and (a,3). Find the value of a.

Answer 1

$\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{a}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{a}-\underset{x_1}{0}}}~~=~~\stackrel{\stackrel{slope}{\downarrow }}{1}\implies \cfrac{3+1}{a}=1\implies 4=a$