Question

Find an equation of the line through the given pair of points (-1,-8) (-6,-9)

The equation of the line is… ___

Answer 1

`(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{-9}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-9}-\stackrel{y1}{(-8)}}}{\underset{run} {\underset{x_2}{-6}-\underset{x_1}{(-1)}}} \implies \cfrac{-9 +8}{-6 +1} \implies \cfrac{ -1 }{ -5 }\implies \cfrac{1}{5}`

`\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}{(-8)}=\stackrel{m}{\cfrac{1}{5}}(x-\stackrel{x_1}{(-1)})\implies y+8=\cfrac{1}{5}(x+1) \\\\\\ y+8=\cfrac{1}{5}x+\cfrac{1}{5}\implies y=\cfrac{1}{5}x+\cfrac{1}{5}-8\implies y=\cfrac{1}{5}x-\cfrac{39}{5}`