Question

What equation can be used to represent the relationship shown 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}{2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{2}}} \implies \cfrac{ 2 }{ 2 } \implies 1`

`\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}{5}=\stackrel{m}{ 1}(x-\stackrel{x_1}{2}) \\\\\\ y-5=x-2\implies {\Large \begin{array}{llll} y=x+3 \end{array}}`