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