Question

Write an equation of the line below

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}{-8}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-8)}}} \implies \cfrac{-8}{0 +8} \implies \cfrac{ -8 }{ 8 } \implies - 1`

`\begin{array}c \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}{4}=\stackrel{m}{- 1}(x-\stackrel{x_1}{(-8)}) \implies y -4 = - 1 ( x +8) \\\\\\ y-4=-x-8\implies {\Large \begin{array}{llll} y=-x-4 \end{array}}`