Proportionality (mathematics) - Inverse Proportionality

The concept of inverse proportionality can be contrasted against direct proportionality. Consider two variables said to be "inversely proportional" to each other. If all other variables are held constant, the magnitude or absolute value of one inversely proportional variable will decrease if the other variable increases, while their product (the constant of proportionality k) is always the same.

Formally, two variables are inversely proportional (or varying inversely, or in inverse variation, or in inverse proportion or in reciprocal proportion) if one of the variables is directly proportional with the multiplicative inverse (reciprocal) of the other, or equivalently if their product is a constant. It follows that the variable y is inversely proportional to the variable x if there exists a non-zero constant k such that

The constant can be found by multiplying the original x variable and the original y variable.

As an example, the time taken for a journey is inversely proportional to the speed of travel; the time needed to dig a hole is (approximately) inversely proportional to the number of people digging.

The graph of two variables varying inversely on the Cartesian coordinate plane is a hyperbola. The product of the X and Y values of each point on the curve will equal the constant of proportionality (k). Since neither x nor y can equal zero (if k is non-zero), the graph will never cross either axis.