Question

Write an equation of the line in the graph.

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}{-4}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-3}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{-4}-\underset{x_1}{(-8)}}} \implies \cfrac{-3 +4}{-4 +8} \implies \cfrac{ 1 }{ 4 }`

`\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}{ \cfrac{ 1 }{ 4 }}(x-\stackrel{x_1}{(-8)}) \implies y +4 = \cfrac{ 1 }{ 4 } ( x +8) \\\\\\ y+4=\cfrac{ 1 }{ 4 }x+2\implies {\Large \begin{array}{llll} y=\cfrac{ 1 }{ 4 }x-2 \end{array}}`