Direct Variation
I can decide whether a relationship is a direct variation and find its constant.
The problem this sheet solves
Direct variation gets taught as linear, and the two are not the same. The defining feature is a CONSTANT RATIO, which means nothing may be added, and the graph must pass through the origin. A student testing only one pair of values finds a constant and stops, which is exactly how y = 2x + 3 gets misclassified. This sheet makes students divide y by x for SEVERAL pairs, so a ratio that moves is caught by the test rather than by intuition. Passing through the origin is treated as a second, independent check, and the sheet includes non-examples that look convincingly linear so the distinction has to be applied.
The key rule
Direct variation is y = kx with nothing added. Divide y by x for every pair: one constant answer means direct variation, and the graph must pass through (0, 0).
Same ratio every time, and through the origin.
Watch out
The mistake: A student calls y = 2x + 3 a direct variation because it graphs as a straight line.
The fix: Test the ratio: (1, 5) gives 5 and (2, 7) gives 3.5. It moves, so it is not direct variation, and the line misses (0, 0).
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.