Question

Write the equation of the line in slope intercept form that goes

through the points (5,8)
and (7,16).

Answer 1

`(\stackrel{x_1}{5}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{16}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{16}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{5}}}\implies \cfrac{8}{2}\implies 4 \\\\\\ \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}{8}=\stackrel{m}{4}(x-\stackrel{x_1}{5}) \\\\\\ y-8=4x-20\implies y=4x-12`