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What is the average rate of change of y(x)

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over the interval -5 < x < -2?

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So this is x = -5.

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When x = -5, y(x) = 6.

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And when x = -2, y(x) = 0.

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So to figure of the average rate of change –

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so the average rate of change of y(x) with respect –

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and we can assume it’s with respect to x –

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with respect to x –

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And let me make that a little bit neater.

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– with respect to x …

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This is going to be the change in y(x) over that interval

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over the change in x over that interval.

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And the shorthand for 'change' is this triangle symbol ‘delta.’

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Delta y –

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I’ll just write y.

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I could write delta y(x).

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It’s delta y –

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– change in y over our change in x.

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That’s going to be our average rate of change

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over this interval.

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So how much did y change over this interval?

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So y went from a 6 to a 0.

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So let's say that this is –

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We can kind of view this as our end point, right over here.

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So this is our 'end' and this is our 'start.'

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And we could have done it the other way around,

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and we would [have gotten an identical] result.

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Since this is higher up on the list,

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let’s call this the 'start.'

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And this is – the x is a lower value.

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We'll call that our 'start.' This is our 'end.'

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So we start at 6.

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We end at 0.

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So our change in y is gong to be -6.

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We went down by 6 in the y direction.

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It's -6. You could say that's a 0 - 6.

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And our change in x –

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well, we were at -5, and we go up to -2.

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We increased by 3.

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So we increased by 3.

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So we went –

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When we increase x by 3, we decreased y(x) by 6.

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Or, if we want to simplify this right over here,

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(-6)/3 is the same thing as -2.

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So our average rate of change of y(x)

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over the interval from -5 to -2 is -2.

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Every time, on average, x increased by 1, y [changed] by -2.