To find the average rate of change between two points, we need to calculate the slope of the line connecting those points. In this case, we need to find the slope of the line connecting the points (3, f(3)) and (5, f(5)).
Let's assume we have a function f(x) and we want to find the average rate of change between x=3 and x=5. We can use the following formula to calculate the average rate of change:
Average rate of change = (f(5) - f(3)) / (5 - 3)
This formula gives us the slope of the line connecting the two points. We can then interpret this slope as the average rate of change between the two points.
For example, if f(x) = 2x + 1, then:
f(3) = 2(3) + 1 = 7
f(5) = 2(5) + 1 = 11
So, the average rate of change between x=3 and x=5 is:
Average rate of change = (11 - 7) / (5 - 3) = 2
Therefore, the average rate of change between x=3 and x=5 is 2.