Question

Find the equation of the like containing (8,5) (-10,-4)

Answer 1

$\bf (\stackrel{x_1}{8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-10}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{-10}-\underset{x_1}{8}}}\implies \cfrac{-9}{-18}\implies \cfrac{1}{2}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{\cfrac{1}{2}}(x-\stackrel{x_1}{8}) \\\\\\ y-5=\cfrac{1}{2}x-4\implies y=\cfrac{1}{2}x+1$