Question

Write an equation in slope intercept form for the line that passes through (5, -8) and (11, 10)

Answer 1

$\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{11}~,~\stackrel{y_2}{10}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{10-(-8)}{11-5}\implies \cfrac{10+8}{11-5}\implies \cfrac{18}{16}\implies \cfrac{9}{8}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-8)=\cfrac{9}{8}(x-5)\implies y+8=\cfrac{9}{8}(x-5) \\\\\\ y+8=\cfrac{9}{8}x-\cfrac{45}{8}\implies y=\cfrac{9}{8}x-\cfrac{45}{8}-8\implies y=\cfrac{9}{8}x-\cfrac{109}{8}$