[tex]\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ -3}}\quad ,&{{ 4}})\quad
% (c,d)
&({{ -5}}\quad ,&{{ 1}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-4}{-5-(-3)}\implies \cfrac{1-4}{-5+3}
\\\\\\
\cfrac{-3}{-2}\implies \cfrac{3}{2}[/tex]
[tex]\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-4=\cfrac{3}{2}[x-(-3)]
\\\\\\
y-4=\cfrac{3}{2}(x+3)\implies y-4=\cfrac{3}{2}x+\cfrac{9}{2}\implies y=\cfrac{3}{2}x+\cfrac{9}{2}+4
\\\\\\
y=\cfrac{3}{2}x+\cfrac{17}{2}[/tex]
