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## Average rate of change

# Worked example: average rate of change from table

CCSS.Math:

## Video transcript

What is the average
rate of change of y of x over the
interval negative 5 is less than x is
less than negative 2? So this is x is
equal to negative 5. When x is equal to negative
5, y of x is equal to 6. And when x is equal to negative
2, y of x is equal to 0. So to figure out the
average rate of change, so the average rate
of change, of y of x, with respect--
and we can assume it's with respect to x-- let me
make that a little bit neater-- this is going to
be the change in y of x over that interval over the
change of x of that interval. And the shorthand for change
is this triangle symbol, delta. Delta y-- I'll just write y. I could write delta y of x. It's delta y. Change in y over
our change in x. That's going to be our
average rate of change over this interval. So how much did y change
over this interval? So y went from a 6 to a 0. So let's say that we
can kind of view this as our endpoint right over here. So this is our end. This is our start. And we could have done
it the other way around. We would get a
consistent result. But since this is
higher up on the list, let's call this the start. And the x is a lower value. We'll call that our start. This is our end. So we start at 6. We end at 0. So our change in y is
going to be negative 6. We went down by 6
in the y direction. It's negative 6. You could say that's 0 minus 6. And our change in x, well,
we are at negative 5, and we go up to negative 2. We increased by 3. So when we increased x by
3, we decreased y of x by 6. Or if we want to simplify
this right over here, negative 6 over 3 is the
same thing as negative 2. So our average
rate of change of y of x over the interval from
negative 5 to negative 2 is negative 2. Every time, on
average, x increased 1, y went down by negative 2.