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Inverse Variation

Concept

Inverse Variation

Inverse variation, or inverse proportionality, occurs when two variables, xx and y,y, have a relationship such that their product is constant. This relationship is often written with one of the variables isolated on the left-hand side.

k=xyy=kxk=xy\quad \Leftrightarrow \quad y=\dfrac{k}{x}

The constant, k,k, is called the constant of variation or the proportionality constant.

The constant of variation may be any real number except 0.0.

Examples of Inverse Variation
Example Rule Comment
The gas pressure in a sealed container if the container's volume is changed. p=kVp=\dfrac{k}{V} kk depends on the amount of gas there is in the container and the temperature.
The time, t,t, it takes to travel a given distance at various speeds, s.s. t=dst=\dfrac{d}{s} The constant of variation, d,d, is the distance.

Inverse variation is closely related to other types of variation.