Find the average rate of change for the function over the given interval. Y = 3/x-2 between x = 4 and x = 7?

The average rate of change is given by (∆Y)/(∆X), where ∆Y is the difference between the Y values at the end points of the interval, and ∆X is the length of the interval.
Y(7) = 3/7-2 = -11/7
Y(4) = 3/4-2 = -5/4
(∆Y)/(∆X) = (-11/7 - (-5/4))/(7 - 4) = (-9/28)/(3) = -3/28
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Perhaps you intend y=3/(x-2). In that case, (∆y)/(∆x) = (3/5 - 3/2)/(7-4) = -3/10.