Question

Write an equation in slope -intercept form of the line that passes through (4,6) and (-8,3)

Answer 1

$\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{-8}-\underset{x_1}{4}}}\implies \cfrac{-3}{-12}\implies \cfrac{1}{4}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{\cfrac{1}{4}}(x-\stackrel{x_1}{4}) \\\\\\ y-6=\cfrac{1}{4}x-1\implies y=\cfrac{1}{4}x+5$