Question

E table shows a function. Is the function linear or nonlinear?

x y
8 3
13 8
18 13

Answer 1

The function represented by the given points (8, 3), (13, 8), and (18, 13) is linear, as the rate of change (slope) between the points is consistent.

Step-by-step explanation:

To determine whether a function is linear or nonlinear, one can look at the rate of change between the points. If the rate of change is consistent, the function is linear.

Looking at the table with points (8, 3), (13, 8), and (18, 13), we can calculate the rate of change (slope) between each pair of points.

From (8, 3) to (13, 8), the change in y is 8 - 3 = 5 and the change in x is 13 - 8 = 5, which gives us a slope of 5/5 = 1.

From (13, 8) to (18, 13), the change in y is 13 - 8 = 5 and the change in x is 18 - 13 = 5, again giving us a slope of 5/5 = 1.

Since the slope between the points is consistent, the function is linear.