Question

what is the equation in slope-intercept form for a line that passes through the points (-3, 6) and (9, 10)

Answer 1

`(\stackrel{x_1}{-3}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{10}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{10}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{9}-\underset{x_1}{(-3)}}} \implies \cfrac{ 4 }{9 +3} \implies \cfrac{ 4 }{ 12 } \implies \cfrac{1}{3}`

`\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}{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 {\Large \begin{array}{llll} y=\cfrac{1}{3}x+7 \end{array}}`