Question

What is the equation of a line that has a slope of -1/2 and contains the point (8,1)?

Answer 1

$(\stackrel{x_1}{8}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ -\cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{-\cfrac{1}{2}}(x-\stackrel{x_1}{8}) \\\\\\ y-1=-\cfrac{1}{2}x+4\implies y=-\cfrac{1}{2}x+5$