[tex]\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~{{ -2}} &,&{{ 2}}~)
% (c,d)
&&(~{{ 5}} &,&{{ 3}}~)
\end{array}
\\\\\\
% slope = m
slope = {{ m}}\implies
\cfrac{\stackrel{rise}{{{ y_2}}-{{ y_1}}}}{\stackrel{run}{{{ x_2}}-{{ x_1}}}}\implies \cfrac{3-2}{5-(-2)}\implies \cfrac{3-2}{5+2}\implies \cfrac{1}{7}[/tex]
[tex]\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-2=\cfrac{1}{7}[x-(-2)]
\implies
y-2=\cfrac{1}{7}(x+2)
\\\\\\
y-2=\cfrac{1}{7}x+\cfrac{2}{7}\implies y=\cfrac{1}{7}x+\cfrac{2}{7}+2\implies y=\cfrac{1}{7}x+\cfrac{16}{7}[/tex]
