Question

Find the equation of the line passing through the points (3,3) and (4,5). y = [? ]x +[ ?]

Answer 1

$\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{3}}}\implies \cfrac{2}{1}\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{2}(x-\stackrel{x_1}{3}) \\\\\\ y-3=2x-6\implies y=2x-3$