Question

What equation in the point slope form matches the graph line shown

A• y+6= 4/5 (x+3)
B•y-2=-3/4(x-6)
C•y-6=4/5(x-3)
B•y-5=-2/3(x+9)

Answer 1

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

`(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{(-6)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-3)}}} \implies \cfrac{-2 +6}{2 +3} \implies \cfrac{ 4 }{ 5 }`

`\begin{array}ll \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}{(-6)}=\stackrel{m}{\cfrac{4}{5}}(x-\stackrel{x_1}{(-3)}) \implies y +6= \cfrac{4}{5} (x +3)`