Overview:
Suppose we have to lines with the slopes 
and 
respectively. We can tell the relative position of two as following:
- The two lines are parallel if
(except when the two lines are vertical, because slope is undefined for vertical lines) - The two lines are perpendicular if
(the proof can be seen here)
By using this informations one can solve problems involving finding the equation of line passing through a point and parallel (or perpendicular) to another line.
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Parallel and Perpendicular Lines