Question

Write the slope-intercept form of the equation of the line through the given point (5, -2) and (0, -5)

Answer 1

$\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{5}}}\implies \cfrac{-5+2}{-5}\implies \cfrac{-3}{-5}\implies \cfrac{3}{5}$

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