Skill: variation

Variation Tutor Help

Stuck on variation? Review the core ideas, read answers to common questions, and send a question to a tutor.

1 Quick recap

Direct: y = kx (ratio y/x constant). Inverse: y = k/x (product xy constant). Joint: y = kxz. Always find k from the known point first — then predict. Test tables with both y/x and xy.

Core ideas

Direct y = kx → k = y/x.
Inverse y = k/x → k = xy.
Joint y = kxz → k = y/(xz).
Two steps: find k, then predict.
Check tables with y/x AND xy before naming the type.

2 Questions students ask

The questions a tutor hears most about this skill.

How do I tell direct from inverse in a table?

Compute y/x down each row: constant means direct. Compute xy: constant means inverse. In the table (2, 12), (3, 8), (4, 6), the products are all 24 — inverse. Never guess from “looks proportional”.

Why does inverse variation never touch the axes?

y = k/x is undefined at x = 0 (division by zero), and y = 0 would need k = 0. The hyperbola approaches both axes forever without reaching them.

Is y = 3x + 1 a variation?

No — the +1 breaks it. Variation models have no added constant: doubling x must double y (direct) or halve y (inverse). y = 3x + 1 fails that test.

3 Ask a tutor

Stuck on a problem? Send it in — a tutor will walk you through it.

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