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This example should also give you some idea of how radio stations work -- by amplitude modulation (AM), or frequency modulation (FM).
Secant line slopes thus represent an approximation to the slope of the tangent line: we think of them as an "average change" over an interval, whereas the tangent line is the "change" over a point!
The secant line slopes represent an average rate of change of a function, whereas the tangent line slopes represent an instantaneous rate of change of the function.
But it's all about slopes! That's made clear by the important equations on p. 104 and 105.
This Secant Demo is one provided by Wolfram, maker of Mathematica. It's downloadable. Try downloading the author code and the cdf, and using them. The cdf file has "Download Source Code" as an option. Try downloading that. If you're not successful, here it is.
What the author is hoping that you'll notice is the fact that, as you make h small (bring the two points on the secant line closer to the point of tangency), the secant line will converge to the tangent line.
This is passing to the limit, the limit $h \to 0$.
More specifically, the slope of the secant line converges to the slope of the tangent line (which is the derivative of the function at the point $x_0$).
Make sure that this point is clear before you leave today! If not, call me over to discuss.
If you have time (and interest!) you might want to try to change the function, and otherwise play with the code (perhaps to suit one of the examples in your textbook). See if you can! It's a challenge....