Question

Determine the equation of a line in slope-intercept form that passes through the points (3, 6) and (6, 8)

Answer 1

`\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{8}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{8-6}{6-3}\implies \cfrac{2}{3} \\\\\\ \begin{array}c \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-6=\cfrac{2}{3}(x-3) \\\\\\ y-6=\cfrac{2}{3}x-2\implies y=\cfrac{2}{3}x+4`