Find and graph the tangent line to the curve represented by the following pair of parametric equations:

at **t = 1.5** using the TI-85 graphing calculator.

[Press here to see animation again!]

- If you are not familiar with the graphing of functions on the TI-85, then first read the Initial Setup page from Little's Basic Guide to the TI-85.
- In order to graph a system of parametric equations, the calculator must be
in the
**PARAM**graphing mode. To change into this mode, press 2nd MODE. You should see a screen similar to the following: - Using the arrow keys, move the blinking cursor to the
**PARAM**item of the fifth row and press the ENTER key. - Press the EXIT key.
- Press the GRAPH key and then pick
**E(t)=**by pressing the F1 key. - If necessary, keep pressing F4 key until only
the two items
**xt1=**and**yt1=**appear on the screen. - At the prompt
**xt1=**, type in**t ^ 2 + 1**and press the ENTER key.

- At the prompt
**yt1=**, type in**t ^ 3 - t**and press the ENTER key.

- The range settings for the graph above are
- Pick the item
**GRAPH**from the menu by pressing the F5 key. - Press the MORE key so that
**MATH**appears on the menu. Pick**MATH**by pressing the F1 key. - Press the MORE key again so that
**TANLN**appears on the menu. Pick**TANLN**by pressing the F1 key. - Press the right arrow key until the value
**t = 1.5**appears in the left lower corner of the screen:A blinking cursor indicates the point on the curve corresponding to

**t = 1.5**. The coordinates of the point,**x = 3.25**and**y = 1.875**appear at the bottom of the screen. - Press the ENTER key to draw the tangent line and
to calculate its slope which appears at the bottom of the screen,
**dy/dx = 1.9166666667**.Hence, the equation of the tangent line is

**y - 1.875 = 1.9166...(x - 3.25)**.