Which of the following functions are linear?
Function A
x 3 6 9 12 15
y 9 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? Function A x 3 6 9 12 15 y 9 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
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To determine which functions are linear, we need to check if the relationship between ( x ) and ( y ) is consistent with the formula of a linear function, which can be expressed as ( y = mx + b ) where ( m ) is the slope and ( b ) is the y-intercept.
Function A:
– The ( y ) values (9, 36, 81, 144, 225) increase at a varying rate:
( 36-9 = 27 ), ( 81-36 = 45 ), ( 144-81 = 63 ), ( 225-144 = 81 ).
The differences are not constant, indicating it’s not linear.
Function B:
– The ( y ) values (8, 16, 24, 32, 40) increase with a constant difference of 8:
( 16-8 = 8 ), ( 24-16 = 8 ), ( 32-24 = 8 ), ( 40-32 = 8 ).
Since the differences are constant, this function is linear.
Thus, the correct answer is Function B.
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