Question

What are the steps to find the equation of a line that passes through (-5,6) and (-2,-9)?​

Answer 1

`(\stackrel{x_1}{-5}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-9}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-9}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{(-5)}}}\implies \cfrac{-15}{-2+5}\implies \cfrac{-15}{3}\implies -5`

`\begin{array} \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}{6}=\stackrel{m}{-5}(x-\stackrel{x_1}{(-5)}) \\\\\\ y-6=-5(x+5)\implies y-6=-5x-25\implies y=-5x-19`