Question

Please write a linear equation that passes through (5,2) and (6,4)!

Answer 1

`(\stackrel{x_1}{5}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{5}}} \implies \cfrac{ 2 }{ 1 } \implies 2`

`\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}{2}=\stackrel{m}{ 2}(x-\stackrel{x_1}{5}) \\\\\\ y-2=2x-10\implies {\Large \begin{array}{llll} y=2x-8 \end{array}}`