Thursday, September 11, 2008

Average rate of change

Is the average rate of change for the green function from 0 to 12 the same as the average rate of change for the red function from 0 to 12?

That was part of our discussion during today's class...does the average rate of change vary if the endpoints remain the same?

We then were able to rediscover the "forumla" for the slope of a line given two points.

Finally, we were able to find the slope of linear equations in Standard Form.

Any comments, questions, or observations from today's class?


Vanessa Sanchez (pd. 2) said...

A little clarification from today’s class:

When you have standard form, Ax+By=C, we decided that the slope would be –A/B. We wanted to determine if we could find a positive slope just by looking at standard form. I think that if A is neg. then B has to be pos., and if A is pos. then B must be neg. (Basically they have to be opposites.) This is because when you rearrange this equation into slope-intercept form you have to subtract the Ax.

Mr. Marti said...

You are correct.

In order to have a line with positive slope, A and B have to have opposite signs. So, as you mentioned and explained by the need to rearrange the A, if A is pos. then B has to be neg.

The only "gotcha" is that (and I thought I recalled you mentioning this in class) is that in "true" Standard Form, A is by definition always a non-negative integer.

vanessa s. said...

Yeah, after I posted this I realized I forgot that A has to be positive. oops. =]