Question

Write an equation to match this 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}{3}~,~\stackrel{y_1}{15})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{35}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{35}-\stackrel{y1}{15}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{3}}} \implies \cfrac{ 20 }{ 4 } \implies 5`

`\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}{15}=\stackrel{m}{ 5}(x-\stackrel{x_1}{3}) \\\\\\ y-15=5x-15\implies {\Large \begin{array}{llll} y=5x \end{array}}`