The table shows a function. Is the function linear or nonlinear?
x y
0 0
8 1/4 8 1/4
10 10
The function is linear because the change in y is proportional to the change in x. As x increases by 10, y also increases by 10.
To determine if the function is linear or nonlinear, we need to check if the rate of change is constant. Let's calculate the rate of change between the given points.
The rate of change between (0, 0) and (8 1/4, 8 1/4) is:
(8 1/4 - 0) / (8 1/4 - 0) = 8 1/4 / 8 1/4 = 1
The rate of change between (8 1/4, 8 1/4) and (10, 10) is:
(10 - 8 1/4) / (10 - 8 1/4) = 1 3/4 / 1 3/4 = 1
Since the rate of change between any two points is the same (1), the function is linear.