Which of the following tables represents a proportional relationship?x 12 18 30 36 y 4 8 16 24x 12 18 30 36 y 4 8 16 24 x 12 18 30 36 y 10 15 25 30 x 12 18 30 36 y 10 15 25 30 x 8 12 16 24 y 10 15 25 30x 8 12 16 24 y 10 15 25 30 x 12 18 30 36 y 12 24 36 48
The correct table that represents a proportional relationship is:
x 12 18 30 36
y 4 8 16 24
A proportional relationship is one in which the ratio between the values of the two variables remains constant. To determine which table represents a proportional relationship, we need to check if the ratio between the x-values and the y-values is consistent.
Let's calculate the ratios for each table:
For the first table, the ratios are:
12/4 = 3
18/8 = 2.25
30/16 = 1.875
36/24 = 1.5
The ratios are not consistent, so the first table does not represent a proportional relationship.
For the second table, the ratios are:
12/4 = 3
18/8 = 2.25
30/16 = 1.875
36/24 = 1.5
The ratios are consistent, so the second table represents a proportional relationship.
For the third table, the ratios are:
12/10 = 1.2
18/15 = 1.2
30/25 = 1.2
36/30 = 1.2
The ratios are consistent, so the third table represents a proportional relationship.
For the fourth table, the ratios are:
8/10 = 0.8
12/15 = 0.8
16/25 = 0.64
24/30 = 0.8
The ratios are not consistent, so the fourth table does not represent a proportional relationship.
Based on these calculations, the tables that represent a proportional relationship are the second table:
x 12 18 30 36
y 4 8 16 24
and the third table:
x 12 18 30 36
y 10 15 25 30
To determine if a table represents a proportional relationship, we need to check if the ratio between the values of x and y is constant. In other words, if we divide the values of y by the corresponding values of x, we should get the same quotient for all the pairs of values.
Let's calculate the ratios for each table:
Table 1:
x 12 18 30 36
y 4 8 16 24
Ratios: 4/12 = 1/3, 8/18 = 4/9, 16/30 = 8/15, 24/36 = 2/3
The ratios are not constant, so this table does not represent a proportional relationship.
Table 2:
x 12 18 30 36
y 4 8 16 24
Ratios: 4/12 = 1/3, 8/18 = 4/9, 16/30 = 8/15, 24/36 = 2/3
The ratios are constant for all the pairs of values, so this table represents a proportional relationship.
Table 3:
x 12 18 30 36
y 10 15 25 30
Ratios: 10/12 = 5/6, 15/18 = 5/6, 25/30 = 5/6, 30/36 = 5/6
The ratios are constant for all the pairs of values, so this table represents a proportional relationship.
Table 4:
x 8 12 16 24
y 10 15 25 30
Ratios: 10/8 = 5/4, 15/12 = 5/4, 25/16 = 25/16, 30/24 = 5/4
The ratios are constant for the first three pairs of values, but not for the last pair. Therefore, this table does not represent a proportional relationship.
Table 5:
x 12 18 30 36
y 12 24 36 48
Ratios: 12/12 = 1, 24/18 = 4/3, 36/30 = 6/5, 48/36 = 4/3
The ratios are not constant, so this table does not represent a proportional relationship.
Based on the calculations, only the second table (x 12 18 30 36, y 4 8 16 24) and the third table (x 12 18 30 36, y 10 15 25 30) represent proportional relationships.