Question

Find the equation of the line through the points (-2,4) and (3,-5) using point-slope form. Then rewrite the equation in slope-intercept form.

Answer 1

`(\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-2)}}} \implies \cfrac{-5 -4}{3 +2}\implies \cfrac{-9}{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}{4}=\stackrel{m}{-\cfrac{9}{5}}(x-\stackrel{x_1}{(-2)})\implies y-4=-\cfrac{9}{5}(x+2) \\\\\\ y-4=-\cfrac{9}{5}x-\cfrac{18}{5}\implies y=-\cfrac{9}{5}x-\cfrac{18}{5}+4\implies y=-\cfrac{9}{5}x+\cfrac{2}{5}`