Question

The line AB passes through the points A(2, -1) and (6, k). The slope of AB

is 5. Work out the value of k.

Answer 1

`A(\stackrel{x_1}{2}~,~\stackrel{y_1}{-1})\qquad B(\stackrel{x_2}{6}~,~\stackrel{y_2}{k}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{k}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}} \implies \cfrac{k +1}{4} ~~ = ~~\stackrel{\stackrel{\textit{sllope of AB}}{\downarrow }}{5}\implies k+1=20\implies \boxed{k=19}`