Question

What is the equation of the line that passes through (-3, 6) and (3, 4)?

Answer 1

`\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-3)}}}\implies \cfrac{-2}{3+3}\implies \cfrac{-2}{6}\implies -\cfrac{1}{3}`

`\bf \begin{array}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}{3}}[x-\stackrel{x_1}{(-3)}]\implies y-6=-\cfrac{1}{3}(x+3) \\\\\\ y-6=-\cfrac{1}{3}x-1\implies y=-\cfrac{1}{3}x+5`