Slopes of parallel and perpendicular lines, writing their equations through a given point, perpendicular bisectors, and proving shapes with slopes.
Parallel lines: equal slopes
Perpendicular lines: opposite reciprocals
To get the perpendicular slope, flip the fraction and change the sign. The opposite reciprocal of \(\frac{2}{3}\) is \(-\frac{3}{2}\); of \(-4\) it's \(\frac{1}{4}\).
The perpendicular bisector of a segment
The perpendicular bisector of \(\overline{AB}\) passes through the midpoint and is perpendicular to the segment. Every point on it is equidistant from \(A\) and \(B\).
Proving shapes with slopes
Slopes let you prove facts about polygons drawn on the coordinate plane.
Practice
Quick check
A line has slope \(-\frac{2}{3}\). What is the slope of a line perpendicular to it?
Flip and change the sign: \(\frac{3}{2}\).
Quick check
Which line is parallel to \(y = 5x - 1\)?
Parallel lines have the same slope, \(5\).
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