Question

Y = mx + b to find the equation of the line that passes through the points (−6, 1) and (3, 4).

Answer 1

$\bf (\stackrel{x_1}{-6}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-6)}}}\implies \cfrac{3}{3+6}\implies \cfrac{3}{9}\implies \cfrac{1}{3}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{\cfrac{1}{3}}[x-\stackrel{x_1}{(-6)}] \implies y-1=\cfrac{1}{3}(x+6) \\\\\\ y-1=\cfrac{1}{3}x+2\implies y=\cfrac{1}{3}x+3$