Question

Which of the equations below best describes 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}{0}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{0}}} \implies \cfrac{ 1 }{ 3 }\\`

`\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}{2}=\stackrel{m}{ \cfrac{ 1 }{ 3 }}(x-\stackrel{x_1}{0})\implies y-2=\cfrac{ 1 }{ 3 }x \\\\\\ {\Large \begin{array}{llll} y=\cfrac{ 1 }{ 3 }+2\implies y=\cfrac{2}{6}x+2 \end{array}}`