Question

Write an equation for this graph in slope-intercept

(Please show proof on how u did it i need to show work)

thank u so much (:

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}{7})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{3}}} \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}{7}=\stackrel{m}{ \cfrac{ 1 }{ 3 }}(x-\stackrel{x_1}{3}) \\\\\\ y-7=\cfrac{ 1 }{ 3 }x-1\implies {\Large \begin{array}{llll} y=\cfrac{ 1 }{ 3 }x+6 \end{array}}`