Question

Which of the following tables represent a proportional relationship

A. x 12 18 30 36 y 4 8 1624
B. x 12 18 30 36 y 10 15 25 30
C.x 8 12 1624 y 10 15 25 30
D.x 12 18 30 36 y 12 24 36 48

Answer 1

[AI-generated answer — Bot GPT 3.5]

The table that represents a proportional relationship is:

B. x 12 18 30 36 y 10 15 25 30

In this table, as x increases, y also increases in a consistent ratio.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To determine if a table represents a proportional relationship, we need to check if the ratio between the x-values and the y-values remains constant.

Let's examine each table:

A. x: 12, 18, 30, 36; y: 4, 8, 16, 24
To calculate the ratio, divide the y-values by the corresponding x-values:
4/12 = 1/3
8/18 = 4/9
16/30 = 8/15
24/36 = 2/3

Since the ratios are not consistent, this table does not represent a proportional relationship.

B. x: 12, 18, 30, 36; y: 10, 15, 25, 30
Calculating the ratios:
10/12 = 5/6
15/18 = 5/6
25/30 = 5/6
30/36 = 5/6

The ratios are the same for all values, so this table represents a proportional relationship.

C. x: 8, 12, 16, 24; y: 10, 15, 25, 30
Calculating the ratios:
10/8 = 5/4
15/12 = 5/4
25/16 = 1.5625
30/24 = 1.25

Since the ratios are not consistent, this table does not represent a proportional relationship.

D. x: 12, 18, 30, 36; y: 12, 24, 36, 48
Calculating the ratios:
12/12 = 1
24/18 = 4/3
36/30 = 6/5
48/36 = 4/3

The ratios are the same for all values, so this table represents a proportional relationship.

Therefore, the tables that represent a proportional relationship are B and D.

Answer 3

[AI-generated answer — Explain Bot]

To determine which table represents a proportional relationship, we need to check if there is a constant ratio between the values of x and y.

Let's calculate the ratios for each table:

A. x: 12 ÷ 4 = 3, 18 ÷ 8 = 2.25, 30 ÷ 16 = 1.875, 36 ÷ 24 = 1.5
The ratios are not constant, so Table A does not represent a proportional relationship.

B. x: 12 ÷ 10 = 1.2, 18 ÷ 15 = 1.2, 30 ÷ 25 = 1.2, 36 ÷ 30 = 1.2
The ratios are constant (1.2), so Table B represents a proportional relationship.

C. x: 8 ÷ 10 = 0.8, 12 ÷ 15 = 0.8, 16 ÷ 25 = 0.64, 24 ÷ 30 = 0.8
The ratios are not constant, so Table C does not represent a proportional relationship.

D. x: 12 ÷ 12 = 1, 18 ÷ 24 = 0.75, 30 ÷ 36 = 0.833, 36 ÷ 48 = 0.75
The ratios are not constant, so Table D does not represent a proportional relationship.

Therefore, the table that represents a proportional relationship is Table B.