Question

What is an equation of the line that passes through the points (-3, -2)(−3,−2) and (2, -7)(2,−7)?

Answer 1

`(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-7}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-3)}}} \implies \cfrac{-7 +2}{2 +3} \implies \cfrac{ -5 }{ 5 }\implies -1`

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