Parallel and Perpendicular Lines
I can use slope to decide whether two lines are parallel, perpendicular, or neither.
The problem this sheet solves
Given m = 2/3 a student answers −2/3, having negated without flipping. The answer looks like it has been operated on, which is what makes it stick, and it is wrong for every slope except a handful. Parallel is easy enough that it hides the problem, so the two cases have to be practised together. This sheet gives a check that settles it without recall: multiply the two slopes and see whether you get −1. That single test turns a remembered rule into something a student can verify, and it catches the sign-only error immediately. Parallel and perpendicular are mixed throughout so students decide which relationship applies rather than following instructions.
The key rule
Parallel keeps the slope. Perpendicular flips it AND changes its sign — check by multiplying, which gives −1.
Flip and negate. Both, or neither works.
Watch out
The mistake: For m = 2/3, a student answers −2/3.
The fix: Sign only — flip as well, to −3/2. Products: −1 for that pair, −4/9 for hers.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.