Which table shows a non-proportional linear relationship between x and y?
A
x y
1 3
3 7
5 11
7 15
9 19
B
x y
-5 -50
0 0
5 50
10 100
15 150
C
x y
2 6
3 9
4 12
5 15
6 18
D
x y
-12 24
-5 10
-2 4
5 -10
8 -16
The answer is D.
A non-proportional linear relationship means that the line does not pass through the origin (0,0).
– Table A has a constant difference between y-values, indicating a proportional relationship.
– Table B shows values that maintain a consistent ratio, hence it is proportional as well.
– Table C has a constant ratio (each y-value is 3 times the x-value) and is proportional.
– Table D does not pass through the origin because when x is 0, y is not 0 (the calculated y-value from the trend would be 0, but here we have negative and positive ranges).
Thus, Table D presents a non-proportional linear relationship.