CLICKING HERE WILL OPEN A WINDOW WITH THE SECANT LINE APPLET

The green line always passes through the two green points. If you drag the mouse while holding either button down on a circle, that point will move and the corresponding curve will change accordingly. Clicking on "snap" will move the green points to their nearest integer x-coordinates. You may change the yellow curve to either a parabola, exponential or cubic curve by clicking in the "Change to _______" box.

The green points will, with luck, always remain on the yellow curve. If the points are different, you get a secant line to the curve through those points. If you move one of these points on top of the other, then you should see a message to the right saying what happens in this case. For each of the three possible yellow curves, try to find a relationship between the slope of the resulting line and the x-coordinate where the points coincide.