Question

A line passes through (1, - 1) and (3,5) what is the equation of the line in slope-intercept form?

Answer 1

`(\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{5 +1}{3 -1}\implies \cfrac{6}{2}\implies 3`

`\begin{array}c \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}{3}(x-\stackrel{x_1}{1}) \\\\\\ y+1=3x-3\implies y=3x-4`