Which of the following tables represent a proportional relationship
A. x 4 6 8 10 y 6 9 12 15
B. x 1 4 7 10 y 0 3 6 9
C. x 2 4 6 8 y 3 4 5 6
The table that represents a proportional relationship is C. x 2 4 6 8 y 3 4 5 6.
This is because for every increase of 2 in x, there is a corresponding increase of 1 in y.
To determine whether a table represents a proportional relationship, we need to check if the ratio between the two variables remains constant.
Let's analyze the tables provided:
A. x 4 6 8 10
y 6 9 12 15
The ratio between x and y gives us:
4/6 = 2/3 = 0.67
6/9 = 2/3 = 0.67
8/12 = 2/3 = 0.67
10/15 = 2/3 = 0.67
Since the ratio between x and y is constant (0.67), table A represents a proportional relationship.
B. x 1 4 7 10
y 0 3 6 9
The ratio between x and y gives us:
1/0 = undefined
4/3 = 4/3 = 1.33
7/6 = 7/6 ≈ 1.17
10/9 = 10/9 ≈ 1.11
Since the ratio between x and y is not constant, table B does not represent a proportional relationship.
C. x 2 4 6 8
y 3 4 5 6
The ratio between x and y gives us:
2/3 ≈ 0.67
4/4 = 1
6/5 = 1.2
8/6 ≈ 1.33
Since the ratio between x and y is not constant, table C does not represent a proportional relationship.
Therefore, the table that represents a proportional relationship is A. x 4 6 8 10, y 6 9 12 15.
To determine if a table represents a proportional relationship, we need to check if there is a constant ratio between the values in the x-column and the corresponding values in the y-column.
Let's analyze the three options:
A. x 4 6 8 10 y 6 9 12 15
To find the constant ratio, we can divide the y-values by the x-values:
6/4 = 1.5
9/6 = 1.5
12/8 = 1.5
15/10 = 1.5
Since the ratio between the x and y values is always 1.5, this table represents a proportional relationship.
B. x 1 4 7 10 y 0 3 6 9
Let's calculate the ratios:
0/1 = 0
3/4 = 0.75
6/7 = 0.86
9/10 = 0.9
Since the ratios between the x and y values are not equal, this table does not represent a proportional relationship.
C. x 2 4 6 8 y 3 4 5 6
Calculating the ratios:
3/2 = 1.5
4/4 = 1
5/6 = 0.83
6/8 = 0.75
Since the ratios between the x and y values are not equal, this table does not represent a proportional relationship.
Therefore, only option A represents a proportional relationship.