The constant of variation is a number that relates two variables that are directly proportional to one another. The number represents a fixed ratio between the two variables, describing how they correspondingly increase or decrease. Constants of variation cannot be calculated for linear expressions that involve variables that are equal to multiple arithmetic terms. If the dependent variable does not equal zero when the independent variable equals zero, the two are not constantly varying.
The constant of variation is either the slope or the inverse of the slope in a simple linear equation. Constants in algebraic expressions are values that do not change. When two variables are directly proportional, the increase in one leads to an increase in the other.
Speed and distance are two such variables. As the speed of a moving object increases, the distance traveled in a fixed amount of time increases. In this example, the fixed time is the constant of variation that ties the variables speed and distance together. Fixing the speed and relating the distance traveled to the time elapsed turns this speed into the constant of variation. Pi is the constant of variation in the circle area formula, whereas the two variables are the circle area and the square of the radius.