[tex]\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ -7 &,& -5~)
% (c,d)
&&(~ -5 &,& 4~)
\end{array}
\\\\\\
% slope = m
slope = m\implies
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-(-5)}{-5-(-7)}\implies \cfrac{4+5}{-5+7}\implies \cfrac{9}{2}[/tex]
[tex]\bf \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-5)=\cfrac{9}{2}[x-(-7)]
\\\\\\
y+5=\cfrac{9}{2}(x+7)\impliedby \textit{now let's multiply both sides by }\stackrel{LCD}{2}
\\\\\\
2(y+5)=2\left[ \cfrac{9}{2}(x+7)\right]\implies 2y+10=9(x+7)
\\\\\\
2y+10=9x+63\implies \stackrel{standard~form}{-9x+2y=53}[/tex]
