Question

Find the point-slope equation for

Answer 1

$(\stackrel{x_1}{7}~,~\stackrel{y_1}{-21})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{23}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{23}-\stackrel{y1}{(-21)}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{7}}} \implies \cfrac{23 +21}{-4 -7} \implies \cfrac{ 44 }{ -11 }\implies -4$

$\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-21)}=\stackrel{m}{-4}(x-\stackrel{x_1}{7})\implies y+21=-4(x-7)$