Linear graphs represent the behavior of dependent variables that sit along a straight line with regard to independent variables, while nonlinear graphs represent variables that don't. Common functions that result in nonlinear graphs include quadratic, cubic and exponential functions as well as functions with sudden jumps in value.
Linear graphs represent relationships between an independent variable x and a dependent variable y that can be described by a multiplication of x by a coefficient a such that a one-unit increase in x results in a increase or decrease of a units in y. For example, the speed of a vehicle under constant acceleration has a linear relation with the rate of acceleration such that the speed of the vehicle graphed with respect to time forms a straight line. However, the distance traveled by such a vehicle per second increases over time, so the relationship of time and total distance traveled begins to curve upward rapidly. This is an example of a nonlinear graph.
Nonlinear graphs are commonly encountered whenever a dependent variable is related to an independent variable that is raised to a particular power. These graphs also occur when the rate of change in a variable is dependent on the value of the variable itself, a condition usually described by an exponential function. Radioactive decay and compound interest are examples of common exponential processes that result in nonlinear graphs when depicted visually.