[tex]\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ -2}}\quad ,&{{ 4}})\quad
% (c,d)
&({{ 8}}\quad ,&{{ 10}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{10-4}{8-(-2)}\implies \cfrac{10-4}{8+2}\implies \cfrac{6}{10}
\\\\\\
\cfrac{3}{5}[/tex]
[tex]\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-4=\cfrac{3}{5}[x-(-2)]\implies y-4=\cfrac{3}{5}(x+2)
\\\\\\
y-4=\cfrac{3}{5}x+\cfrac{6}{5}\implies y=\cfrac{3}{5}x+\cfrac{6}{5}+4\implies y=\cfrac{3}{5}x+\cfrac{26}{5}[/tex]
