Chapter 3:Ratio and Proportion, 3.3:Inverse Proportion

What is inverse proportion?

• Two quantities are inversely proportional when one increases while the other decreases in a way that keeps their product constant.

• If one quantity doubles, the other is halved.

• If one quantity triples, the other becomes one-third.

Inverse proportion equation

• y ∝ 1/x means y is inversely proportional to x.

• This can be written as y = k/x.

• k is the constant of proportionality.

Constant of proportionality

• For inverse proportion, the product x × y is always constant.

• The constant is found using k = xy.

Using inverse proportion

• Find the constant of proportionality first.

• Use y = k/x to find the unknown value.

• Make sure the relationship is inverse, not direct.

Inverse proportion graphs

• The graph is a curve called a reciprocal curve.

• It does not pass through the origin.

• As x increases, y gets closer to zero.

Direct vs inverse proportion

• Direct: y = kx, so y/x is constant.

• Inverse: y = k/x, so xy is constant.

Important

• Direct proportion: both quantities change in the same direction.

• Inverse proportion: the quantities change in opposite directions.

• In inverse proportion, multiplying one quantity by a factor means dividing the other by the same factor.