Question

A line passes through the points (

–
1,2) and (3,18). Write its equation in slope-intercept form.

Answer 1

`(\stackrel{x_1}{-1}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{18}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{18}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{(-1)}}} \implies \cfrac{ 16 }{3 +1} \implies \cfrac{ 16 }{ 4 } \implies 4`

`\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}{2}=\stackrel{m}{4}(x-\stackrel{x_1}{(-1)}) \implies y -2 = 4 ( x +1) \\\\\\ y -2 = 4 x +4 \implies {\Large \begin{array}{llll} y = 4 x +6 \end{array}}`