Question

Complete the equation of the line through ( − 8 , 8 ) (−8,8) and ( 1 , − 1 0 ) (1,−10). Use exact numbers.

Answer 1

$\bf (\stackrel{x_1}{-8}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-10}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-10-8}{1-(-8)}\implies \cfrac{-18}{1+8}\implies \cfrac{-18}{9}\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-8=-2[x-(-8)] \implies y-8=-2(x+8) \\\\\\ y-8=-2x-16\implies y=-2x-8$