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.