Question

Find the equation of this line.

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}{-3}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{1}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{(-3)}}} \implies \cfrac{ 2 }{3 +3} \implies \cfrac{ 2 }{ 6 } \implies \cfrac{1}{3}`

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