How do you determine if a function is linear or non linear Linear vs Non Linear How do you determine if a function is linear or non linear

Linear Function

Non Linear Function

How do you tell when you get a set of data points x y 2 7 4 14 6 21 8 28

Linear For it to be linear, the rate of change needs to be the same on all sets of point Change in y over the Change in x, will not differ For it to be linear, you cannot have x raised to any power

The x’s are increasing by 2’s The y’s are increasing by 7 As long as they are all the same increase, it is linear

Linear or Non Linear x y -2 -1 1 3 5

Linear or Non Linear x y 1 -5 2 -7 3 -21

Linear or Non Linear x y 5 -15 8 -11 11 -7 14 -3

Linear or Non Linear x y 1 2 4 3 8

Linear Vs Nonlinear All linear functions can be written in Y = mx + b format Is y = 2x2 + 5 a linear function