Question

Write the equation of the line in fully simplified slope-intercept form.

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}{-4}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-10}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-10}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{(-4)}}} \implies \cfrac{-10 +4}{2 +4} \implies \cfrac{ -6 }{ 6 } \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}{(-4)}) \implies y +4 = -1 ( x +4) \\\\\\ y +4 = - x -4 \implies {\Large \begin{array}{llll} y = - x -8 \end{array}}`