Question

For the function y = 2/7x + 1/3 what is its average rate of change from x = 3 to x = 8?​

Answer 1

The average rate of change for the function y = 2/7x + 1/3 from x = 3 to x = 8 is calculated by finding the differences in y and x values between these points and dividing the former by the latter.

Step-by-step explanation:

To find the average rate of change of the function y = 2/7x + 1/3 from x = 3 to x = 8, we need to calculate the change in y divided by the change in x over this interval. The formula for the average rate of change is given by:

(y2 - y1) / (x2 - x1)

First, we substitute x = 3 into the function to find y1:

y1 = (2/7) * 3 + 1/3

Then, we substitute x = 8 into the function to find y2:

y2 = (2/7) * 8 + 1/3

After calculating these values, we find the difference y2 - y1 and x2 - x1 and divide the former by the latter to determine the average rate of change.

Answer 2

The average rate of change of the function is 37/105.

Step-by-step explanation:

The average rate of change of a function between two points is given by the difference in the function values divided by the difference in the x-values. In this case, the function is y = 2/7x + 1/3. To find the average rate of change from x = 3 to x = 8, we substitute these values into the function and calculate the difference:

y(3) = 2/7(3) + 1/3 = 13/21

y(8) = 2/7(8) + 1/3 = 50/21

Therefore, the average rate of change is (50/21 - 13/21) / (8 - 3) = 37/21 / 5 = 37/105.