Question

What is an equation of the line that passes through the points (3,1) and (-3, -7)

Answer 1

`\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{-7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-7}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{-3}-\underset{x_1}{3}}}\implies \cfrac{-8}{-6}\implies \cfrac{4}{3}`

`\bf \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}{1}=\stackrel{m}{\cfrac{4}{3}}(x-\stackrel{x_1}{3}) \\\\\\ y-1=\cfrac{4}{3}x-4\implies y=\cfrac{4}{3}x-3`