Question

A line passes through the points 3,10 and 6, 16 write the equation of this line in slope-intercept form

Answer 1

$(\stackrel{x_1}{3}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{16}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{16}-\stackrel{y1}{10}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{3}}} \implies \cfrac{ 6 }{ 3 } \implies 2$

$\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{ 2}(x-\stackrel{x_1}{3}) \\\\\\ y-10=2x-6\implies {\Large \begin{array}{llll} y=2x+4 \end{array}}$