Check the picture below.
to get the slope of any line all we need is two points, so we'll use those,
[tex]\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-5)}}}\implies \cfrac{-5}{4+5}\implies -\cfrac{5}{9}[/tex]
[tex]\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-\stackrel{y_1}{3}=\stackrel{m}{-\cfrac{5}{9}}[x-\stackrel{x_1}{(-5)}]\implies y-3=-\cfrac{5}{9}(x+5) \\\\\\ y-3 = -\cfrac{5}{9}x-\cfrac{25}{9}\implies y = -\cfrac{5}{9}x-\cfrac{25}{9}+3\implies y = -\cfrac{5}{9}x+\cfrac{2}{9}[/tex]
