Parallel and Perpendicular Lines
I can use slopes to tell whether two lines are parallel, perpendicular or neither.
What students learn
Students learn to compare slopes to tell parallel, perpendicular or neither, and write a parallel or perpendicular line through a point.
See inside
The key rule
Parallel lines have the same slope; perpendicular slopes are opposite reciprocals, so their product is −1.
m₁ × m₂ = −1
Every line on this sheet can be written y = mx + b: none is vertical.
Watch out
Find the slope of a line perpendicular to y = (3/4)x − 2.
The mistake: −3/4: change the signOnly the sign changed; 3/4 was not flipped.
The fix: −4/3: (3/4)(−4/3) = −1Flip and change the sign: the product is −1.
The mistakes it targets
- Changes only the sign for a perpendicular slope
- Flips the slope but keeps its sign
- Calls slopes with opposite signs perpendicular
- Keeps the old y-intercept for the new line instead of using the point
The interactive Teacher Deck (32 slides, PowerPoint)
- The Learn page taught on screen: 8 fill-in blanks, each filled on its own click as students write it
- The worked example one slide per step (four steps), each with the reason for the step
- Six practice and three apply problems: a your-turn slide with a think-time bar, then the solution one line per click
- Jump buttons on every slide: go straight to any problem, the answer bank or the exit ticket
- Speaker notes on each problem: the question to ask, the worked answer and the common error to listen for
- A completed deck PDF (19 pages) with every slide fully built, to print or post
The student packet (9 pages)
- Learn: guided notes with four definitions, the key rule, a worked example and a Watch Out error pair
- Practice: two warm-up, two standard and two stretch problems, with an answer bank for self-checking that hides three common-mistake decoys
- Apply: one word problem, a reasoning prompt and one error analysis
- Assess: an exit ticket of four items, two per page, with an I-can self-rating
- Homework (page 5): eight new problems, two warm-up, four standard and two stretch
- Answer key (pages 6–7): every problem worked step by step, four common mistakes with what to do about each, and a grading guide, plus the homework key (page 8)
- Color and ink-saver editions of the whole packet
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.