[tex]\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 3}}\quad ,&{{7}})\quad
% (c,d)
&({{ 4}}\quad ,&{{ 9}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{9-7}{4-3}\implies \cfrac{2}{1}\implies 2[/tex]
[tex]\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-7=2(x-3)\implies y-7=2x-6
\\\\\\
y=2x+1\qquad \qquad \qquad \qquad \qquad \qquad \stackrel{standard~form}{-2x+y=1}[/tex]
