Question

Write an equation of the line that passes through the given points. (-2,5) and (1,2)

Answer 1

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

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{-1}[x-\stackrel{x_1}{(-2)}] \\\\\\ y-5=-(x+2)\implies y-5=-x-2\implies y=-x+3$