Slopes of Perpendicular Lines

Two lines are perpendicular if they meet at a right angle — a relationship that shows up everywhere, from the edges of a square to the axes of a graph. The key insight is that their slopes are not just different, but are negative reciprocals of each other: if one line rises steeply, the other must fall just as steeply to cross it at $90^\circ$. This simple condition, $m_1 …