Which table does not show a proportional relationship between xx and yy?
A
xx	yy
55	77
1010	1414
2020	2828
2525	3535
B
xx	yy
44	66
1010	1515
2424	3636
2626	3939
C
xx	yy
55	77
1515	2121
2020	2828
3030	4242
D
xx	yy
1414	1616
1616	1818
2222	2424
2525	2727
Answer

To determine which table does not show a proportional relationship, we need to check if the ratio \(\frac{y}{x}\) is constant for each table. If the ratio is consistent across all pairs, the table shows a proportional relationship.

### Analyzing Each Table:

1. **Table A**:
   - \( \frac{y}{x} = \frac{7}{5} = 1.4 \)
   - \( \frac{14}{10} = 1.4 \)
   - \( \frac{28}{20} = 1.4 \)
   - \( \frac{35}{25} = 1.4 \)
   - **Consistent ratio**: Yes

2. **Table B**:
   - \( \frac{y}{x} = \frac{6}{4} = 1.5 \)
   - \( \frac{15}{10} = 1.5 \)
   - \( \frac{36}{24} = 1.5 \)
   - \( \frac{39}{26} = 1.5 \)
   - **Consistent ratio**: Yes

3. **Table C**:
   - \( \frac{y}{x} = \frac{7}{5} = 1.4 \)
   - \( \frac{21}{15} = 1.4 \)
   - \( \frac{28}{20} = 1.4 \)
   - \( \frac{42}{30} = 1.4 \)
   - **Consistent ratio**: Yes

4. **Table D**:
   - \( \frac{y}{x} = \frac{16}{14} \approx 1.14 \)
   - \( \frac{18}{16} = 1.125 \)
   - \( \frac{24}{22} \approx 1.09 \)
   - \( \frac{27}{25} = 1.08 \)
   - **Inconsistent ratio**: No

### Conclusion:
Table **D** does not show a proportional relationship between \(x\) and \(y\) because the ratio \(\frac{y}{x}\) is not consistent.

**Answer: D**

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Would you like further details on proportional relationships or have any other questions?

### Additional Practice Questions
1. What would make a relationship between \(x\) and \(y\) proportional?
2. Can you determine the constant of proportionality for Table A?
3. If one of the values in Table D changed, could it be made proportional?
4. How would you plot a proportional relationship on a graph?
5. What is the significance of the ratio \(\frac{y}{x}\) in identifying proportional relationships?

**Tip:** A quick way to verify proportionality is to see if each \(\frac{y}{x}\) yields the same constant across all entries.

Which table does not show a proportional relationship between x and y?
A
x   y
5  7
10  14
20  28
25  35
B
x   y
4   6
10  15
24  36
26  39
C
x   y
5   7
15  21
20  28
30  42
D
x   y
14  16
16  18
22  24
25  27

Learn how to identify proportional relationships by examining tables of x and y values. This problem involves analyzing ratios for consistency across four tables to determine which one does not exhibit a proportional relationship, with a step-by-step solution. Suitable for Grades 6-8.

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