Which table shows a proportional relationship between x and y?
A. x y
10 5
18 9
20 15
24 14
B. x y
7 6
10 9
24 23
28 27
C. x y
7 33
10 48
19 93
23 113
D. x y
2 1
66 3
20 10
28 14
A. x y
10 5
18 9
20 15
24 14
In table A, as x increases, y also increases. However, the relationship between x and y is not consistent. For example, when x increases from 10 to 18, y increases from 5 to 9. But when x increases from 18 to 20, y increases from 9 to 15, which is not proportional.
B. x y
7 6
10 9
24 23
28 27
In table B, as x increases, y also increases. Additionally, the relationship between x and y is consistent. For example, when x increases from 7 to 10, y increases from 6 to 9. This consistent relationship indicates that table B shows a proportional relationship between x and y.
C. x y
7 33
10 48
19 93
23 113
In table C, as x increases, y also increases. However, the relationship between x and y is not consistent. For example, when x increases from 7 to 10, y increases from 33 to 48. But when x increases from 10 to 19, y increases from 48 to 93, which is not proportional.
D. x y
2 1
66 3
20 10
28 14
In table D, as x increases, y also increases. However, the relationship between x and y is not consistent. For example, when x increases from 2 to 66, y increases from 1 to 3. But when x increases from 20 to 28, y increases from 10 to 14, which is not proportional.
Therefore, the table that shows a proportional relationship between x and y is B. x = 7, 10, 24, 28 and y = 6, 9, 23, 27.
To determine which table shows a proportional relationship between x and y, we need to check if the ratio of y to x is constant for each value of x.
Let's analyze each table:
A.
The ratio of y to x is:
5/10 = 0.5
9/18 ≈ 0.5
15/20 = 0.75
14/24 ≈ 0.58
Since the ratio is not constant, table A does not represent a proportional relationship.
B.
The ratio of y to x is:
6/7 ≈ 0.86
9/10 = 0.9
23/24 ≈ 0.96
27/28 ≈ 0.96
Since the ratio is not constant, table B does not represent a proportional relationship.
C.
The ratio of y to x is:
33/7 ≈ 4.71
48/10 = 4.8
93/19 ≈ 4.89
113/23 ≈ 4.91
Since the ratio is close to constant for each pair of values, table C represents a proportional relationship.
D.
The ratio of y to x is:
1/2 = 0.5
3/66 ≈ 0.045
10/20 = 0.5
14/28 = 0.5
Since the ratio is not constant, table D does not represent a proportional relationship.
Therefore, the table that shows a proportional relationship between x and y is table C.
To determine if a table shows a proportional relationship between x and y, we need to check if the ratio between the two values remains constant throughout the table.
Let's analyze each table:
A. x y
10 5
18 9
20 15
24 14
To find the ratio between x and y, we divide y by x:
For the first row, 5/10 = 0.5
For the second row, 9/18 = 0.5
For the third row, 15/20 = 0.75
For the fourth row, 14/24 ≈ 0.583
Since the ratio is not constant, table A does not show a proportional relationship between x and y.
B. x y
7 6
10 9
24 23
28 27
For the first row, 6/7 ≈ 0.857
For the second row, 9/10 = 0.9
For the third row, 23/24 ≈ 0.958
For the fourth row, 27/28 ≈ 0.964
Since the ratio is not constant, table B does not show a proportional relationship between x and y.
C. x y
7 33
10 48
19 93
23 113
For the first row, 33/7 ≈ 4.714
For the second row, 48/10 = 4.8
For the third row, 93/19 ≈ 4.895
For the fourth row, 113/23 ≈ 4.913
Since the ratio is approximately constant (around 4.8), table C shows a proportional relationship between x and y.
D. x y
2 1
66 3
20 10
28 14
For the first row, 1/2 = 0.5
For the second row, 3/66 ≈ 0.045
For the third row, 10/20 = 0.5
For the fourth row, 14/28 = 0.5
Since the ratio is constant (0.5), table D shows a proportional relationship between x and y.
Therefore, the tables that show a proportional relationship between x and y are table C and table D.