check the picture below.
that's the line of x = 12, just a straight vertical line, notice the green line, that's parallel to it, and the red line, that's perpendicular to it.
let's pick two points for each to get their slopes, hmm say for the green one (5,2) and (5,4)
[tex]\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{2})\qquad
(\stackrel{x_2}{5}~,~\stackrel{y_2}{4})
\\\\\\
% slope = m
slope = m\implies
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-2}{5-5}\implies \stackrel{und efined}{\cfrac{2}{0}}[/tex]
and for the red one hmmm (3,2) and (7,2)
[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{2})\qquad
(\stackrel{x_2}{7}~,~\stackrel{y_2}{2})
\\\\\\
% slope = m
slope = m\implies
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-2}{7-3}\implies \cfrac{0}{4}\implies 0[/tex]
