Question

Complete the equation of a line that goes through (-9,-9) and (6,0)

Answer 1

`(\stackrel{x_1}{-9}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{0}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{0}-\stackrel{y1}{(-9)}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{(-9)}}} \implies \cfrac{0 +9}{6 +9} \implies \cfrac{ 9 }{ 15 } \implies \cfrac{3}{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}{(-9)}=\stackrel{m}{\cfrac{3}{5}}(x-\stackrel{x_1}{(-9)}) \implies y +9 = \cfrac{3}{5} ( x +9) \\\\\\ y+9=\cfrac{3}{5}x+\cfrac{27}{5}\implies y=\cfrac{3}{5}x+\cfrac{27}{5}-9\implies {\Large \begin{array}{llll} y=\cfrac{3}{5}x-\cfrac{18}{5} \end{array}}`