Example 2: A segment of a straight line through the origin

The parametric curve or trajectory for these parametric equations is a line segment.

$$\left. \begin{array}{lclcl} x &=& f(t) &=& t\\ y &=& g(t) &=& 3t+4\\ \end{array}\right\}\quad 0\leq t\leq 4$$

Any time $x=f(t)$ is the identity function $x=t$ , the parametric curve will be the same as the graph of $y=g(x)$ .

In this case, it is the same as the graph of $y=3x+4$ .