Question

Find the equation of a line that passes through (-2,4) and (1,-2)

Answer 1

$\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-2)}}}\implies \cfrac{-6}{1+2}\implies \cfrac{-6}{3}\implies -2$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-2}[x-\stackrel{x_1}{(-2)}]\implies y-4=-2(x+2) \\\\\\ y-4=-2x-4\implies y = -2x$