Question

Find the slope intercept form.

passes through the points (4,3) and (7,-2)

Answer 1

`(\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{4}}} \implies \cfrac{-2 -3}{7 -4} \implies \cfrac{ -5 }{ 3 }`

`\begin{array} \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}{3}=\stackrel{m}{-\cfrac{5}{3}}(x-\stackrel{x_1}{4}) \\\\\\ y-3=-\cfrac{5}{3}x+\cfrac{20}{3}\implies y=-\cfrac{5}{3}x+\cfrac{20}{3}+3\implies y=-\cfrac{5}{3}x+\cfrac{29}{3}`