Identify the table that demonstrates a proportional relationship.(1 point)
Responses
x y
4 2
9 3
16 4x y 4 2 9 3 16 4
x y
2 10
5 20
6 30x y 2 10 5 20 6 30
x y
8 2
12 3
40 4x y 8 2 12 3 40 4
x y
10 2
15 3
40 8
The table that demonstrates a proportional relationship is the table with x values of 4, 9, and 16 and y values of 2, 3, and 4.
The table that demonstrates a proportional relationship is:
x y
4 2
9 3
16 4
To identify the table that demonstrates a proportional relationship, we need to determine if the ratio between the x-values and the y-values remains constant throughout the table.
Let's analyze each table:
Table 1:
x: 4, 9, 16
y: 2, 3, 4
Ratio for x: 4/9 = 0.44, 9/16 = 0.56
Ratio for y: 2/3 = 0.67, 3/4 = 0.75
Since the ratio between x-values and y-values is not constant, this table does not demonstrate a proportional relationship.
Table 2:
x: 2, 5, 6
y: 10, 20, 30
Ratio for x: 2/5 = 0.4, 5/6 = 0.83
Ratio for y: 10/20 = 0.5, 20/30 = 0.67
Since the ratio between x-values and y-values is not constant, this table does not demonstrate a proportional relationship.
Table 3:
x: 8, 12, 40
y: 2, 3, 4
Ratio for x: 8/12 = 0.67, 12/40 = 0.3
Ratio for y: 2/3 = 0.67, 3/4 = 0.75
Since the ratio between x-values and y-values is not constant, this table does not demonstrate a proportional relationship.
Table 4:
x: 10, 15, 40
y: 2, 3, 8
Ratio for x: 10/15 = 0.67, 15/40 = 0.375
Ratio for y: 2/3 = 0.67, 3/8 = 0.375
Since the ratio between x-values and y-values is constant (approximately 0.67), this table demonstrates a proportional relationship.
Therefore, the correct answer is Table 4.