Question

What is the equation from(2,32) to (38,40

Answer 1

$\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{32})\qquad (\stackrel{x_2}{38}~,~\stackrel{y_2}{40}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{40}-\stackrel{y1}{32}}}{\underset{run} {\underset{x_2}{38}-\underset{x_1}{2}}}\implies \cfrac{8}{36}\implies \cfrac{2}{9}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{32}=\stackrel{m}{\cfrac{2}{9}}(x-\stackrel{x_1}{2})\implies y-32=\cfrac{2}{9}x-\cfrac{4}{9} \\\\\\ y=\cfrac{2}{9}x-\cfrac{4}{9}+32\implies y=\cfrac{2}{9}x\implies +\cfrac{284}{9}$