Algebra 2 · Unit 4 · Topic 4.5
Inverse Variation and Rational Models
Inverse variation has form y = k/x with x ≠ 0 and constant product xy = k.
Definition and explanation
Inverse variation has form y = k/x with x ≠ 0 and constant product xy = k. Rational models also arise when a total quantity is divided by a changing number of units; interpret units and physical domain before predicting.
Worked example
A fixed $360 fee is shared equally among n participants. Each person's share is C(n) = 360/n dollars for positive integer n. Twelve participants pay $30 each, while 18 pay $20 each; the product nC(n) stays $360.
Common mistake
Inverse variation is not a constant decrease in cost for each additional participant.
Key takeaway
Inverse variation has form y = k/x with x ≠ 0 and constant product xy = k.
Explain each step of the worked example, then check the units, signs, and conditions that apply.
Further reading
Topic coverage was checked against the openly available OpenStax Intermediate Algebra 2e, Algebra and Trigonometry 2e, and Introductory Statistics 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.