Question

Which table represents a nonlinear function?

x y
−5 7
​−2​ ​6​
​1 ​5​
7 ​3​

x y
​−2​ ​−1​
​0​ 1
2 ​3​
5 ​6​

x y
​−3​ 3
0 0
6 ​−6​
10 ​−10​

x y
​−7​ ​−3​
​−5​ 0
0 3
4 1

Answer 1

the last one is non-linear

Explanation:

the other 3 tables have all constant (the same) change rates of y change / x change for all their point intervals.

the first table shows for every increase of x by 3, y decreases by 1.

the second table shows for every increase of x by 2, y also increases by 2. that automatically means that this is also 1/1, 3/3, ...

the third table shows for every increase of x by 3, y decreases by 3.

but the fourth table shows a varying change rate from point interval to point interval :

x increases by 2, y increases by 3 : ratio 3/2

x increases by 5, y increases by 3 : ratio 3/5

x increases by 4, y decreases by 2 : ratio -2/4 = -1/2

they are all different.

but for a linear function they must be all equal.