bearing in mind that an x-intercept is when the graph touches the x-axis and when that happens y = 0, and a y-intercept is when the graph touches the y-axis and when that happens x = 0.
[tex]\bf \underset{x-intercept}{(\stackrel{x_1}{-5}~,~\stackrel{y_1}{0})}\qquad \underset{y-intercept}{(\stackrel{x_2}{0}~,~\stackrel{y_2}{-1})} ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{(-5)}}}\implies \cfrac{-1}{0+5}\implies -\cfrac{1}{5}[/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}{0}=\stackrel{m}{-\cfrac{1}{5}}[x-\stackrel{x_1}{(-5)}] \\\\\\ y=-\cfrac{1}{5}(x+5)\implies y = -\cfrac{1}{5}x-1[/tex]
