Question

Complete the equation of the line through (-1,6) and (7,-2)

Answer 1

$\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{(-1)}}}\implies \cfrac{-8}{7+1}\implies \cfrac{-8}{8}\implies -1$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{-1}[x-\stackrel{x_1}{(-1)}] \\\\\\ y-6=-(x+1)\implies y-6=-x-1\implies y=-x+5$