2. If not: If the line isn't parallel to the x-axis and you know one specific angle a which produces a parallel to the x-axis then any arbitrary point will serve as center of the rotation. You'll get a parallel to the x-axis, only the place, where this parallel will be, is changing.At what angle should I rotate the line about another point (x4,y4), to make it parallel to the y axis?
The line has the endpoints A and B;
the red point produces a parallel line to the x-axis (drawn in red)
an the blue point produces a parallel line to the x-axis different from the first parallel.
As you can see your angle a has the same value (but the opposite direction) as the angle formed by the original line and a parallel to the x-axis.