Parametric equations are so important in applied mathematics (engineering, graphics, etc.) that many scientific calculators now come equipped to handle graphing them. Please refer to the following figure to help locate many of the buttons mentioned in this file.

On TI-8X (TI-82, TI-83, TI-84, etc.) calculators, press the mode button (next to the 2nd button) and it will bring up a menu. One row of the menu should say "Func Par Pol Seq". Since we want parametric mode, move the cursor over the Par spot and press enter. That sets your calculator to parametric mode.

Now press the "Y = " button. Notice that you have a line for x1T and y1T, meaning x(t) and y(t) for the first equation. Let's plot the parametric equations for the line segment from (2, -1) to (6, 5). In the previous file, we found that these parametric equations for this situation are x = 2 + 4t and y = -1 + 6t where 0 ≤ t ≤ 1.

Now go to the x1T line. We nee to tell it to do x1T= 2 + 4t . Since we are in parametric mode, type in "2" "+" "4" and then push the X,T,θ,N button (usually the button to the right of the green ALPHA button) and it will automatically put in a T (since it is in parametric mode). So now you have x1T= 2 + 4t .

Next, press ENTER or the down arrow to get to the y1T line. Type in "-1 + 6" (being careful to use the negative sign instead of the subtract sign) and then push the X,T,θ,N button to get the T so it says y1T = -1 + 6T.

Since parametric equations depend on T, we need to go to set up the viewing window go to the WINDOW menu by pressing the WINDOW button (on the top line of the calculator, just below the screen). Notice that the first thing that you see is Tmin and Tmax. In our parametric equations 0 = t = 1. Therefore, on the Tmin line type "0" and then press ENTER or the down arrow so you are on the Tmax line and type "1". The next thing to tell it is the Tstep. Since t goes from 0 to 1, it travels a distance of 1 unit. We would like the calculator to plot many points so lets take that 1 and divide by 50 = 0.02 so that it will plot 50 points. So in the Tstep line type "0.02".

We know we want our line segment to go from (2, -1) to (6, 5) so set Xmin to 0 and X max to 8 (or similar values) and leave the Xscl (X-scale) at 1. Similarly, set Ymin to -2 and Ymax to 7 with Yscl set at 1. Then press the GRAPH button.

Viola! We have a graph of our parametric equations.

You can also press the TRACE button and move around on the line segment. Notice that it won't let you go beyond the endpoints of the line segment. That's because we set the Tmin and Tmax limits to 0 and 1, respectively.