Which of the following functions are linear?
Function A
x 3 6 9 12 15
y 36 81 144 225
Function B
x 5 10 15 20 25
y 8 16 24 32 40
Function A
Function B
Function A and Function B
None of the above
Which of the following functions are linear?
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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.