To determine if the function is linear or nonlinear, we need to check if there is a constant rate of change between any two points.
Let's calculate the rate of change between the first two points:
(1/3, 9) and (5 2/3, 3 2/3)
The change in x is 5 2/3 - 1/3 = 5 1/3
The change in y is 3 2/3 - 9 = -5 1/3
The rate of change is -5 1/3 ÷ 5 1/3 = -1
Now let's calculate the rate of change between the second two points:
(5 2/3, 3 2/3) and (8 1/3, 1)
The change in x is 8 1/3 - 5 2/3 = 2 2/3
The change in y is 1 - 3 2/3 = -2 2/3
The rate of change is -2 2/3 ÷ 2 2/3 = -1
Since the rate of change is constant (-1) between any two points, the function is linear.
The table shows a function. Is the function linear or nonlinear?
x y
1/3 9
5 2/3 3 2/3
8 1/3 1
1 answer