[tex]\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ -3 &,& 4~)
% (c,d)
&&(~ 2 &,& -1~)
\end{array}
\\\\\\
% slope = m
slope = m\implies
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-4}{2-(-3)}\implies \cfrac{-1-4}{2+3}\implies -\cfrac{5}{6}[/tex]
[tex]\bf \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-4=-\cfrac{5}{6}[x-(-3)]
\\\\\\
y-4=-\cfrac{5}{6}(x+3)\implies y-4=-\cfrac{5}{6}x-\cfrac{5}{2}
\\\\\\
y=-\cfrac{5}{6}x-\cfrac{5}{2}+4\implies y=-\cfrac{5}{6}x+\cfrac{3}{2}[/tex]
