Question

What is an equation of the line that passes through the points (5, -6) and (-5, -4)?

Answer 1

`(\stackrel{x_1}{5}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{(-6)}}}{\underset{run} {\underset{x_2}{-5}-\underset{x_1}{5}}}\implies \cfrac{-4+6}{-10}\implies \cfrac{2}{-10}\implies -\cfrac{1}{5}`

`\begin{array}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}{-\cfrac{1}{5}}(x-\stackrel{x_1}{5}) \\\\\\ y+6=-\cfrac{1}{5}(x-5)\implies y+6=-\cfrac{1}{5}x+5\implies y=-\cfrac{1}{5}x-1`