Question

Write an equation that represents (0,-1) and (3,-3​

Answer 1

$\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{0}}}\implies \cfrac{-3+1}{3}\implies -\cfrac{2}{3}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{-\cfrac{2}{3}}(x-\stackrel{x_1}{0}) \\\\\\ y+1=-\cfrac{2}{3}x\implies y=-\cfrac{2}{3}x-1$