Inverse Proportion Formula and Examples

Learn how inverse proportion works using y=kxy = \frac{k}{x}and how to find the constant k. Let’s get started! 🚀

Inverse Proportion Formula and Examples - introduction visual

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Inverse proportion with a definition, notation showing y is proportional to 1 divided by x, and the formula y = k divided by x.Inverse proportion example y ∝ 1/x: x=6 gives y=8, so k=48 and y=12 when x=4.Worked example of inverse proportion y ∝ 1/x²: x=3 gives y=8, so k=72 and y=2 when x=6.Inverse proportion example n ∝ 1/√r: n=12 when r=9, so k=36 and n=9 when r=16.

🛎️ What Is Inverse Proportion?

  • Inverse proportion means the product stays constant. For example, if x is doubled, y is halved, so xy stays the same.
  • In exams, multiply the variables together to get the constant k. For example, if x = 3 and y = 8, then k = 3 × 8 = 24.

🛎️ Example: Inverse Proportion to x

  • If y is inversely proportional to x, write xy = k.
  • Multiply the given pair to find k first, then substitute the x value to find the wanted y value.

🛎️ Example: Inverse Proportion to x²

  • If y is inversely proportional to x², write x²y = k.
  • Multiply y by x² to find k, then substitute the x value to find the wanted y value.

🛎️ Example: Inverse Proportion to √x

  • If y is inversely proportional to √x, write √x · y = k.
  • Multiply √x by y to find k, then substitute the x value to find the wanted y value.

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