Question

Write an explicit function for the line that contains the points: (-7,5) and (6, -21).

Answer 1

$(\stackrel{x_1}{-7}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-21}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-21}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-7)}}}\implies \cfrac{-26}{6+7}\implies \cfrac{-26}{13}\implies -2$

$\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{-2}(x-\stackrel{x_1}{(-7)}) \\\\\\ y-5=-2(x+7)\implies y-5=-2x-14\implies y=-2x-9$