INSTRUCTOR: For this video, what I want to do is show you how to find two sets of parametric equations for the given rectangular equation. So the easiest one to work with is to let x equal t. So I'm just going to define my x-coordinate as the equation t. And then what I want to do is I want to replace x in the given equation with whatever I chose x to equal in terms of t. 

So we would say that y equals 3 times t minus 5. So my two parametric equations would just be x equals t and y equals 3t minus 5. So this is one acceptable answer. There are many acceptable answers because you can basically let x equal any function, and then all you have to do is replace it into there. So the other one that I picked-- and like I said, you could pick anything. I just happened to pick this one. I just said, let x equal t minus 2. 

And so now all we would have to do is replace x with the t minus 2. And so we would say that y equals 3 times t minus 2 minus 5. Now what we want to do is simplify this equation. So would distribute the 3n. So I have 3t minus 6 minus 5, which ends up giving me y equals 3t minus 11. 

So another acceptable parametric equation that I could use is that x equals t minus 2 and y equals 3t minus 11. There really are an unlimited number of possibilities because you can pick x to be anything. You can define it as in terms of any expression of t. And then once you plug it into the given rectangular equation, you can find what the equivalent y expression is. 

So with this, you don't have to limit the kinds of equations that you have. There are multiple correct answers. As always, thanks for watching. If you have any questions, please let me know. If there are additional topics you need me to cover, please let me know that as well.