**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.