Question

What is an equation in slope intercept form for the line that passes through the points (1, -3) and (3,1)

Answer 1

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

`\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}{(-3)}=\stackrel{m}{ 2}(x-\stackrel{x_1}{1}) \implies y +3 = 2 ( x -1) \\\\\\ y+3=3x-2\implies {\Large \begin{array}{llll} y=2x-5 \end{array}}`