Theorem 1.9: Given a line whose equation is
and a point whose coordinates are
the equation of the unique line through the point, perpendicular to the line, is
Proof: By Theorem 1.8, there will be a unique line through the point perpendicular to the line whose equation is y = mx + b.Since this line is to be perpendicular to the line whose equation is y = mx + b, its slope will be the negative reciprocal of m or -1/m. If we substitute -1/m for the slope in the formula for the y intercept in Theorem 1.3, we get
If we substitute this into the y = mx + b form of the equation for the perpendicular line, we get the desired result.