Question

What is the slope-intercept form equation of the line that passes through (5,7) and (8,22)

Answer 1

$\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\qquad(\stackrel{x_2}{8}~,~\stackrel{y_2}{22})\\\\\\ slope = m\implies\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{22-7}{8-5}\implies \cfrac{15}{3}\implies 5\\\\\\ \begin{array}{|c|ll}\cline{1-1}\textit{point-slope form}\\\cline{1-1}\\y-y_1=m(x-x_1)\\\\\cline{1-1}\end{array}\implies y-7=5(x-5)\\\\\\y-7=5x-25\implies y=5x-18$