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Inversely proportional

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College Algebra

Definition

Two quantities are inversely proportional if their product is constant. When one quantity increases, the other decreases in such a way that the product remains unchanged.

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5 Must Know Facts For Your Next Test

  1. In an inverse proportion, if $x$ and $y$ are the two quantities, then $x \cdot y = k$, where $k$ is a constant.
  2. The graph of an inversely proportional relationship is a hyperbola.
  3. If $y$ is inversely proportional to $x$, then $y = \frac{k}{x}$ for some constant $k$.
  4. As one variable approaches zero, the other variable approaches infinity (and vice versa).
  5. Inverse proportionality can be applied to modeling real-world scenarios like speed and travel time at a constant distance.

Review Questions

  • What is the general form of an equation representing two inversely proportional quantities?
  • How does the graph of an inversely proportional relationship look?
  • If $x \cdot y = 12$, what is y when x = 3?
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