Question

I need the equation

Answer 1

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

`(\stackrel{x_1}{3}~,~\stackrel{y_1}{13})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{5}-\stackrel{y1}{13}}}{\underset{\textit{\large run}} {\underset{x_2}{15}-\underset{x_1}{3}}} \implies \cfrac{ -8 }{ 12 } \implies - \cfrac{2}{3}`

`\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}{13}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{3}) \\\\\\ y-13=- \cfrac{2}{3}x+2\implies {\Large \begin{array}{llll} y=- \cfrac{2}{3}x+15 \end{array}}`