check the picture below.
any parallel line to y = 12, like the red one and the green one there, will have the same slope as y = 12, what is the that slope anyway?
well, let's pick any two points y = 12 passes by, hmmmmm say 2, 12 and 4, 12
[tex]\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ 2 &,& 12~)
% (c,d)
&&(~ 4 &,& 12~)
\end{array}
\\\\\\
% slope = m
slope = m\implies
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{12-12}{4-2}\implies \cfrac{0}{2}\implies 0[/tex]
