Parametric Equations


By: Stephen Bismarck

Explore x = t+1 , y = 2t-1


If this parametric equation is graphed from [0,10] for t the graph looks like this

It looks like a line segment

If the range is increased to [-10,10], what happens to the graph?


The line segment is bigger, including more negative values, but not a complete line.

How could we make this a line?

We could make the range from but we can't graph infinity

We can replace the infinities with a really big number like 5,000,000 and see what happens


It looks like this is a complete line, but if the screen is expanded you'll see it is only a segment

If we solve for t in both of the equations let's see what we get

t = x-1 and t =1/2 (y+1)

x-1 = 1/2 (y+1)

2x -2 = y+1

y = 2x -3


As you can see some parametric equations are only peices of a function