[tex]\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ 5}}\quad ,&{{ 7}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{7}{2}
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-7=\cfrac{7}{2}(x-5)\implies y-7=\cfrac{7}{2}x-\cfrac{35}{2}
\\\\\\
y=\cfrac{7}{2}x-\cfrac{35}{2}+7\implies \stackrel{standard~form}{-\cfrac{7}{2}x+y=-\cfrac{21}{2}}[/tex]
