This exploration will look at parametric equation.
"A parametric equation is an equation that introduces a third
variable, *t*, which is called a parameter. By writing
both *x* and *y* as functions of *t*, you obtain
a parametric equation." -- This paragraph was taken from
__Calculus__ by Larson, et.al., 5th edition.

Now let us consider the parametric equation

We will start off by letting *a* = *b*
= 0 and look at the two different values for k.

Ex.

Ex.

Graphing these equations for t > 0 we see
that the equations start at the origin and are linear equations
with *k *equal to the slopes of the lines.

If we solve for *t* in terms of x in the
original equation and plug that value into the y function we get

We can see that this parametric equation is
actually a linear function with slope *k* and y-intercept
(*b - ka*). Here is an example of another parametric
equation:

Ex.