The Perpendicular Slope
Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 34 of 64.
Two lines are perpendicular when they meet at a right angle. To find the slope of a perpendicular line, flip the fraction and change the sign. The slope perpendicular to 2/3 is -3/2. The slope perpendicular to 2, which is 2/1, is -1/2. As a rule:
m2 = -1/m1
When you multiply two perpendicular slopes, you always get -1. You can use this to check that two lines are at right angles.
Why does the fraction flip? A slope is rise over run. When you turn a line by a quarter turn, the rise becomes the run and the run becomes the rise, and one of them changes sign. A horizontal line has slope 0. The line perpendicular to it is vertical, and a vertical line has no slope.
Challenge
MediumA line is perpendicular to y = 3/4x + 1. Perpendicular slopes multiply to -1, so its slope m satisfies 3/4 m = -1. Find m.
Try it yourself
Solve for m
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Graphs & Systems
1The Coordinate Plane
Two Numbers, One PointThe Four QuadrantsPoints on the AxesMirror PointsRecap: The Plane4Slope-Intercept Form
y = mx + bThe Starting HeightWrite the EquationSolve for yDraw From Any FormRecap: y = mx + b7Parallel & Perpendicular
Same Slope, Never MeetThe Perpendicular SlopeA Right-Angle LineRecap: Two Relations2From Rule to Line
A Rule Makes PointsThe Points Line UpOn the Line or Not?Between the DotsRecap: Rule to Line