Question

which of the following tables represents a proportional relationship?
a.

x	24	28	32	36
y	72	85	96	108

b.

x	6	12	18	24
y	18	36	54	72

c.

x	6	7	8	9
y	18	36	54	72

d.

x	24	25	26	27
y	72	54	36	18

Explanation:

Step1: Recall proportional relationship rule

For a proportional relationship, the ratio \(\frac{y}{x}\) (or \(\frac{x}{y}\)) must be constant for all pairs of \(x\) and \(y\) values. So we calculate \(\frac{y}{x}\) for each table.

Step2: Analyze Table A

For Table A:

• When \(x = 24\), \(y = 72\), \(\frac{y}{x}=\frac{72}{24}=3\)
• When \(x = 28\), \(y = 85\), \(\frac{y}{x}=\frac{85}{28}\approx3.04\) (not equal to 3)

So Table A is not proportional.

Step3: Analyze Table B

For Table B:

• When \(x = 6\), \(y = 18\), \(\frac{y}{x}=\frac{18}{6}=3\)
• When \(x = 12\), \(y = 36\), \(\frac{y}{x}=\frac{36}{12}=3\)
• When \(x = 18\), \(y = 54\), \(\frac{y}{x}=\frac{54}{18}=3\)
• When \(x = 24\), \(y = 72\), \(\frac{y}{x}=\frac{72}{24}=3\)

All ratios are 3, so this is a proportional relationship. Let's check other tables to be sure.

Step4: Analyze Table C

For Table C:

• When \(x = 6\), \(y = 18\), \(\frac{y}{x}=\frac{18}{6}=3\)
• When \(x = 7\), \(y = 36\), \(\frac{y}{x}=\frac{36}{7}\approx5.14\) (not equal to 3)

So Table C is not proportional.

Step5: Analyze Table D

For Table D:

• When \(x = 24\), \(y = 72\), \(\frac{y}{x}=\frac{72}{24}=3\)
• When \(x = 25\), \(y = 54\), \(\frac{y}{x}=\frac{54}{25}=2.16\) (not equal to 3)

So Table D is not proportional.

Answer:

B.

x	6	12	18	24