# How do you find two different parametric equations for rectangular equation given: y = 6x - 1?

Oct 26, 2017

There are infinitely many ways of parameterizing a curve:

#### Explanation:

The simplest parametrization is to put $x = t$, which gives:

$\left\{\begin{matrix}x = t \\ y = 6 t - 1\end{matrix}\right.$

Another option would be $6 x = t$, giving:

$\left\{\begin{matrix}x = \frac{t}{6} \\ y = t - 1\end{matrix}\right.$

And as a bonus why not use 2x=6tt

$\left\{\begin{matrix}x = 3 t \\ y = 18 t - 1\end{matrix}\right.$