Which of the following tables represents a proportional relationship?(2 points)Responsesx12183036y481624x 12 18 30 36 y 4 8 16 24 x12183036y10152530 x 12 18 30 36 y 10 15 25 30x8121624y10152530x 8 12 16 24 y 10 15 25 30x12183036y12243648
The table that represents a proportional relationship is:
x 12 18 30 36
y 4 8 16 24
To determine which table represents a proportional relationship, we need to check the ratio between the values of x and y in each table.
Let's calculate the ratios for each table:
Table 1 (x: 12, 18, 30, 36 | y: 4, 8, 16, 24):
- Ratio between x and y:
- For x = 12, y = 4 -> ratio = 12/4 = 3
- For x = 18, y = 8 -> ratio = 18/8 = 2.25
- For x = 30, y = 16 -> ratio = 30/16 = 1.875
- For x = 36, y = 24 -> ratio = 36/24 = 1.5
Table 2 (x: 12, 18, 30, 36 | y: 10, 15, 25, 30):
- Ratio between x and y:
- For x = 12, y = 10 -> ratio = 12/10 = 1.2
- For x = 18, y = 15 -> ratio = 18/15 = 1.2
- For x = 30, y = 25 -> ratio = 30/25 = 1.2
- For x = 36, y = 30 -> ratio = 36/30 = 1.2
Table 3 (x: 8, 12, 16, 24 | y: 10, 15, 25, 30):
- Ratio between x and y:
- For x = 8, y = 10 -> ratio = 8/10 = 0.8
- For x = 12, y = 15 -> ratio = 12/15 = 0.8
- For x = 16, y = 25 -> ratio = 16/25 = 0.64
- For x = 24, y = 30 -> ratio = 24/30 = 0.8
Table 4 (x: 12, 18, 30, 36 | y: 12, 24, 36, 48):
- Ratio between x and y:
- For x = 12, y = 12 -> ratio = 12/12 = 1
- For x = 18, y = 24 -> ratio = 18/24 = 0.75
- For x = 30, y = 36 -> ratio = 30/36 = 0.83
- For x = 36, y = 48 -> ratio = 36/48 = 0.75
Based on the ratios calculated, we can see that only Table 2 has a constant ratio of 1.2 for all values of x and y, indicating a proportional relationship. Therefore, Table 2 represents a proportional relationship.
The table that represents a proportional relationship is:
x 12 18 30 36
y 4 8 16 24