Question

Find the value of k so that the line passing through a pair of points has the given slope.

(1, k) and (4, 1), slope = -2

k =?

Answer 1

`\hspace{34em}|\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{k})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) ~\hspace{10em} \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{k}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{1}}}~~ ~~\stackrel{\stackrel{slope}{\downarrow }}{-2} \\\\\\ \cfrac{1-k}{3}= -2\implies 1-k=-6\implies -k=-7\implies k = \cfrac{-7}{-1}\implies \boxed{k = 7}`