Question

Find an equation of the line passing through each of the following pairs of points. a (−3, 1), (0, 3)

Answer 1

$\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{(-3)}}}\implies \cfrac{2}{0+3}\implies \cfrac{2}{3}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{\cfrac{2}{3}}[x-\stackrel{x_1}{(-3)}]\implies y-1=\cfrac{2}{3}(x+3) \\\\\\ y-1=\cfrac{2}{3}x+2\implies y=\cfrac{2}{3}x+3$