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}) ~\hfill \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{ 4 }{ -4 } \implies - 1`

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