When scientists talk about a mathematical model for a real-world phenomenon, they often mean a function that describes the dependence of one physical quantity on another. For instance, the model may describe the population of an animal species as a function of time or the pressure of a gas as a function of its volume. In this section we study a kind of modeling that occurs frequently in the sciences, called variation.

 Direct Variation

One type of variation is called direct variation; it occurs when one quantity is a constant multiple of the other. We use a function of the form f(x) = kx to model this dependence.

Recall that the graph of an equation of the form y = mx + b is a line with slope m and y-intercept b. So the graph of an equation y = kx that describes direct variation is a line with slope k and y-intercept 0

Inverse Variation

Inverse variation: