Which table shows a proportional relationship between x and y? A. x y 2 4 3 6 4 9 B. x y 3 4 9 16 15 20 C. x y 4 12 5 15 6 18 D. x y 1 4 2 8 3 15
The table that shows a proportional relationship between x and y is C. x y 4 12 5 15 6 18.
To determine which table shows a proportional relationship between x and y, we need to check if the ratio of y to x is consistent for every pair of values.
Let's calculate the ratios for each table:
For Table A:
First pair: 4/2 = 2
Second pair: 6/3 = 2
Third pair: 9/4 = 2
Since all the ratios are equal to 2, Table A represents a proportional relationship.
For Table B:
First pair: 4/3 ~ 1.33
Second pair: 16/9 ~ 1.78
Third pair: 20/15 ~ 1.33
The ratios are not consistent, so Table B does not represent a proportional relationship.
For Table C:
First pair: 12/4 = 3
Second pair: 15/5 = 3
Third pair: 18/6 = 3
Since all the ratios are equal to 3, Table C represents a proportional relationship.
For Table D:
First pair: 4/1 = 4
Second pair: 8/2 = 4
Third pair: 15/3 = 5
The ratios are not consistent, so Table D does not represent a proportional relationship.
Therefore, the tables that show a proportional relationship between x and y are A and C.
To determine which table shows a proportional relationship between x and y, we need to check if the ratio of y to x remains constant throughout the table.
A. For table A, the ratio of y to x is not constant. When x increases by 1, y increases by 2, which means the ratio of y to x changes.
B. For table B, the ratio of y to x is constant. When x increases by 3, y increases by 4, maintaining a ratio of 4:3.
C. For table C, the ratio of y to x is not constant. When x increases by 1, y increases by 3, which means the ratio of y to x changes.
D. For table D, the ratio of y to x is not constant. When x increases by 1, y increases by 4, which means the ratio of y to x changes.
Therefore, the table that shows a proportional relationship between x and y is Table B: x y 3 4 9 16 15 20.