Question

Write the point slope form of the line given 2 points on the line . through ( 5, - 1 ) and ( -5 , - 3 )

Answer 1

`\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{-5}-\underset{x_1}{5}}}\implies \cfrac{-3+1}{-10}\implies \cfrac{-2}{-10}\implies \cfrac{1}{5}`

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