Question

What is the slope intercept equation for the following line.

Answer 1

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

`(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-2)}}} \implies \cfrac{-4 +2}{2 +2} \implies \cfrac{ -2 }{ 4 } \implies - \cfrac{ 1 }{ 2 }`

`\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}{(-2)}=\stackrel{m}{- \cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{(-2)}) \implies y +2= -\cfrac{ 1 }{ 2 } (x +2) \\\\\\ y+2=-\cfrac{ 1 }{ 2 }x-1\implies {\Large \begin{array}{llll} y=-\cfrac{ 1 }{ 2 }x-3 \end{array}}`