Question

Find the slope intercept form of the equation of the line through-2,2 and 2,-5.

Answer 1

$\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-2)}}}\implies \cfrac{-7}{2+2}\implies -\cfrac{7}{4}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{-\cfrac{7}{4}}[x-\stackrel{x_1}{(-2)}]\implies y-2=-\cfrac{7}{4}(x+2) \\\\\\ y-2=-\cfrac{7}{4}x-\cfrac{7}{2}\implies y=-\cfrac{7}{4}x-\cfrac{7}{2}+2\implies y=-\cfrac{7}{4}x-\cfrac{3}{2}$