Parametric equations

What you'll learn

1. 1

   Imagine you're drawing a curve on a graph, but instead of y = f(x), both x and y are controlled by a third variable, t — like a puppet master pulling strings!

2. 2

   What does the variable t usually represent in parametric equations?

3. 3

   Here's a simple example: x = t + 1, y = 2t. As t goes from 0 to 3, the point (x, y) moves along a straight line. Watch the path!

4. 4

   Let's find the Cartesian equation (just x and y) from x = t + 1, y = 2t.

5. 5

   Try it yourself! For x = 3t, y = t², find y in terms of x.

6. 6

   For x = 3t, what is t equal to?

7. 7

   If x = 3t and y = t², what is the Cartesian equation?