2.6Slopes of Parallel and Perpendicular Lines
Quick Answer
Parallel lines have equal slopes (m₁ = m₂). Perpendicular lines have slopes that are negative reciprocals (m₁ · m₂ = −1). Use these relationships to classify lines given their equations or two points.
Essential Question
How does slope provide an algebraic test for whether two lines are parallel or perpendicular?
Learning Goals
- 1Calculate slope from two points or an equation.
- 2Determine if lines are parallel using slope.
- 3Determine if lines are perpendicular using slope.
- 4Classify pairs of lines as parallel, perpendicular, or neither.
Key Vocabulary
Slope
m = (y₂−y₁)/(x₂−x₁); the rate of change of a line.
Negative reciprocal
If m = a/b, its negative reciprocal is −b/a; perpendicular slopes are negative reciprocals.
Full lesson content coming soon
Worked examples, guided practice problems, a workbook, quiz, and downloadable PDF resources will be added to this lesson in Phase 2. The learning goals and vocabulary above reflect the complete lesson scope.