by **santaclaus** on Tue Mar 10, 2009 1:14 am

Suppose you wnated to show your students that it is precisely the coefficient of t in y=at +b that determines the "steepness" of its graph. In no more than three complete sentences, explain how you might go about showing this. Assume that the notions of "slope" and of "average rat of change of a function" have NOT been defined, so please do not refer to them.

1. I was thinking of stating, "if you have a point (t_{1}, y_{1}) and another point (t_{2},y_{2}), take the y's and subtract them and divide by this by two t's and subtract them like so: y_{1}-y_{2} divided by t_{1}-t_{2} (I can't format division)

I'm having trouble explaining this - without formally referring to slope -- any ideas?