In this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. The parameter is an independent variable that both $x$ and $y$ depend on, and as the parameter increases, the values of $x$ and $y$ trace out a path along a plane curve. For example, if the parameter is $t$ (a common choice), then $t$ might represent time. Then $x$ and $y$ are defined as functions of time, and $\left(x\left(t\right),y\left(t\right)\right)$ can describe the position in the plane of a given object as it moves along a curved path.