Question

Write a linear equation that passes theough the poiny (3,1) and (9,3) in slope intercept form

Answer 1

`(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{3}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{1}}}{\underset{\textit{\large run}} {\underset{x_2}{9}-\underset{x_1}{3}}} \implies \cfrac{ 2 }{ 6 } \implies \cfrac{1}{3}`

`\begin{array}ll \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}) \\\\\\ y-1=\cfrac{1}{3}x-1\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x \end{array}}`