[tex]\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~{{ -5}} &,&{{ -1}}~)
% (c,d)
&&(~{{ 5}} &,&{{ -5}}~)
\end{array}
\\\\\\
% slope = m
slope = {{ m}}\implies
\cfrac{\stackrel{rise}{{{ y_2}}-{{ y_1}}}}{\stackrel{run}{{{ x_2}}-{{ x_1}}}}\implies \cfrac{-5-(-1)}{5-(-5)}\implies \cfrac{-5+1}{5+5}\implies \cfrac{-4}{10}
\\\\\\
-\cfrac{2}{5}[/tex]
[tex]\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-1)=-\cfrac{2}{5}[x-(-5)]
\\\\\\
y+1=-\cfrac{2}{5}(x+5)\implies y+1=-\cfrac{2}{5}x-\cfrac{2}{\underline{5}}\cdot \underline{5}\implies y+1=-\cfrac{2}{5}x-2
\\\\\\
y+1-1=-\cfrac{2}{5}x-2-1\implies y=-\cfrac{2}{5}x-3[/tex]
