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The Perpendicular Slope

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 34 of 64.

Perpendicular lines meet at a right angle, and their slopes trade places with a twist: flip the fraction and the sign. Against slope 2/3 the perpendicular slope is -3/2; against slope 2 (which is 2/1) it is -1/2. In one rule:

m2 = -1/m1

Multiplied together, perpendicular slopes always give -1: a quick check that two lines really are at right angles.

The geometry behind the flip: turning a rise-over-run step by a quarter turn swaps rise with run and sends one of them negative. Flat and vertical are the extreme pair, slope 0 against no slope at all.

Challenge

A line is perpendicular to y = 3/4x + 1. Find its slope m.

Try it yourself

y = 3/4x + 1

Solve for m

Test yourself

This 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 Point The Four Quadrants Points on the Axes Mirror Points Recap: The Plane

4Slope-Intercept Form

y = mx + b The Starting Height Write the Equation Solve for y Draw From Any Form Recap: y = mx + b

7Parallel & Perpendicular

Same Slope, Never MeetThe Perpendicular SlopeA Right-Angle Line Recap: Two Relations

10Systems by Graphing

Two Lines, One Answer Solve by Drawing Check the Crossing When Lines Never Cross Recap: By Graphing

2From Rule to Line

A Rule Makes Points The Points Line Up On the Line or Not?Between the Dots Recap: Rule to Line

5Point-Slope Form

A Point and a Slope From Two Points Flat or Vertical Through Draw From a Point Recap: Point-Slope

8Function Notation

The Name of a Rule Inputs With Signs Find the Input The Graph of f Recap: f(x)

11Solving Systems Exactly

Substitution Isolate First Elimination Scale, Then Add Three Unknowns Two Numbers, Two Facts Recap: Two Methods