Lesson 4: Parallel and Perpendicular Lines
Duration of Days: 1
Lesson Objective
Students will be able to identify and create equations for parallel and perpendicular lines by analyzing their slopes, recognizing that parallel lines have identical slopes while perpendicular lines have negative reciprocal slopes.
How can you determine if two lines will ever intersect just by looking at their equations?
What is a "negative reciprocal," and why is it necessary for creating a 90 degree angle (perpendicularity)?
If two lines have the same y-intercept but different slopes, can they be parallel?
Parallel Lines: Lines in the same plane that never intersect and have the same slope.
Perpendicular Lines: Lines that intersect at a right angle (90 degrees); their slopes are negative reciprocals (e.g., m = 2 and m = -1/2).
Intersection: The point where two lines cross.
8.EE.B.6: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line.
Target C.5: The student finds the equation y = mx + b for a line.
Description: Students will use the Parallel and Perpendicular Lines Stoplight Activity to classify pairs of equations and practice writing new equations that satisfy specific geometric conditions.
Purpose: To deepen students' understanding of slope as a structural property of lines.
DOK Level: Level 2 (Skill/Concept) – Identifying and calculating slopes; Level 3 (Strategic Thinking) – Constructing equations for lines that must meet specific geometric criteria.
Reciprocal Only: Students often flip the fraction but forget to change the sign for perpendicular slopes (or vice versa).
Vertical/Horizontal Slopes: Difficulty recognizing that a slope of 0 (horizontal) and an undefined slope (vertical) are perpendicular.
Scaffolding: Provide a "Reciprocal Table"
Extension: Challenge students to find a line parallel to a given one that passes through a specific, non-zero coordinate.
Exit Ticket