The table shows a function. Is the function linear or nonlinear?
x y
3 20
9 18
15 16
linear or nonlinear
its lnear
Apologies for the previous response. You are correct, the given table shows a linear function.
To determine if the function is linear or nonlinear, we can observe the behavior of the y-values as x-values change.
For a function to be linear, the change in y-values should be consistent and proportional to the change in x-values. In other words, if the function is linear, the ratio of the change in y to the change in x should be constant.
Let's calculate the ratios using the given table:
For the first pair of points (3, 20) and (9, 18):
Change in y = 18 - 20 = -2
Change in x = 9 - 3 = 6
Ratio = -2 / 6 = -1/3
For the second pair of points (9, 18) and (15, 16):
Change in y = 16 - 18 = -2
Change in x = 15 - 9 = 6
Ratio = -2 / 6 = -1/3
We can see that the ratio (-1/3) is the same for both pairs of points. Therefore, the function is linear since the change in y is consistent and proportional to the change in x.