Question

Use an equation to find the value of k

so that the line passing through (1,3)
and (5,k)
has a slope of 2.

Answer 1

`(\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{k}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{k}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{1}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ 2 }\implies \cfrac{k-3}{4}=2 \\\\\\ k-3=8\implies \boxed{k=11}`