Question

This table shows a function.

(-16, -41)
(-15, -20)
(-7, -2)
(-5, 5)
(2, 1)
(13, 10)
What is the average rate of change over the interval 2 ≤ x ≤ 137
A. -11/9
B. -9/11
C. 9/11
D. 11/9

Answer 1

Answer: Choice C) 9/11

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Step-by-step explanation:

Finding the average rate of change over the interval 2 ≤ x ≤ 13 is the exact same as finding the slope of the line through the points (2,1) and (13,10)

`(x_1,y_1) = (2,1) \text{ and } (x_2,y_2) = (13,10)\\\\m = (y_(2) - y_(1))/(x_(2) - x_(1))\\\\m = (10 - 1)/(13 - 2)\\\\m = (9)/(11)\\\\`

The slope of the line through (2,1) and (13,10) is 9/11 which is also the rate of change we're looking for.