explaining steepness in 3 sentences

[santaclaus]

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 (t₁, y₁) and another point (t₂,y₂), take the y's and subtract them and divide by this by two t's and subtract them like so: y₁-y₂ divided by t₁-t₂ (I can't format division)

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

[stapel_eliz]

Your method feels somewhat formulaic, and may not get the idea of "steepness" across. It might be better to use something like a discussion of steps, ramps, and "how far up you get for every step over you go"...?

[DAiv]

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.

Further to Eliz's reply, since we have three sentences to explain it, I'd probably use one sentence each for when t is positive, zero, and negative.


DAiv