Which of the following functions are linear?

To determine if a function is linear, we need to check if the change in ( y ) is proportional to the change in ( x ) across the values.

Function A:

– The values for ( y ) are: 36, 81, 144, 225.
– The changes are:

– From 36 to 81: change = 45

– From 81 to 144: change = 63

– From 144 to 225: change = 81

– The changes are not constant, indicating a non-linear relationship.

Function B:

– The values for ( y ) are: 8, 16, 24, 32, 40.
– The changes are:

– From 8 to 16: change = 8

– From 16 to 24: change = 8

– From 24 to 32: change = 8

– From 32 to 40: change = 8

– The changes are constant, indicating a linear relationship.

Thus, the correct answer is Function B.

In summary, Function A is not linear, while Function B is linear.