[tex]\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 1}}\quad ,&{{ 5}})\quad
% (c,d)
&({{ -2}}\quad ,&{{ 3}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{3-5}{-2-1}\implies \cfrac{-2}{-3}\implies \cfrac{2}{3}[/tex]
[tex]\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-5=\cfrac{2}{3}(x-1)\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
y-5=\cfrac{2}{3}x-\cfrac{2}{3}\implies -\cfrac{2}{3}x+y=5-\cfrac{2}{3}\implies \stackrel{\textit{standard form}}{-\cfrac{2}{3}x+y=\cfrac{13}{3}}[/tex]
