Which table has a constant of proportionality between 
\[y\] and 
\[x\] of 
\[10\]?
Choose 1 answer:
Choose 1 answer:
(Choice A, Incorrect)   
\[x\]	
\[y\]
\[2\]	
\[20\]
\[12\]	
\[132\]
\[22\]	
\[220\]

Incorrect
\[x\]	
\[y\]
\[2\]	
\[20\]
\[12\]	
\[132\]
\[22\]	
\[220\]
This table does not show a proportional relationship, so it does not have a constant of proportionality.
(Choice B)   
\[x\]	
\[y\]
\[5\]	
\[20\]
\[7\]	
\[30\]
\[10\]	
\[40\]

B
\[x\]	
\[y\]
\[5\]	
\[20\]
\[7\]	
\[30\]
\[10\]	
\[40\]
(Choice C)   
\[x\]	
\[y\]
\[9\]	
\[90\]
\[14\]	
\[140\]
\[24\]	
\[240\]

C
\[x\]	
\[y\]
\[9\]	
\[90\]
\[14\]	
\[140\]
\[24\]	
\[240\]


The constant of proportionality \( k \) between \( y \) and \( x \) can be found using the formula:

\[
k = \frac{y}{x}
\]

We need to determine which table consistently has \( k = 10 \) across all pairs of \( (x, y) \).

### Choice A:
- For \( (x = 2, y = 20) \), \( k = \frac{20}{2} = 10 \)
- For \( (x = 12, y = 132) \), \( k = \frac{132}{12} = 11 \)
- For \( (x = 22, y = 220) \), \( k = \frac{220}{22} = 10 \)

The values of \( k \) are not consistent (10, 11, 10), so this table is **not** proportional.

### Choice B:
- For \( (x = 5, y = 20) \), \( k = \frac{20}{5} = 4 \)
- For \( (x = 7, y = 30) \), \( k = \frac{30}{7} \approx 4.29 \)
- For \( (x = 10, y = 40) \), \( k = \frac{40}{10} = 4 \)

The values of \( k \) are also not consistent (4, 4.29, 4), so this table is **not** proportional.

### Choice C:
- For \( (x = 9, y = 90) \), \( k = \frac{90}{9} = 10 \)
- For \( (x = 14, y = 140) \), \( k = \frac{140}{14} = 10 \)
- For \( (x = 24, y = 240) \), \( k = \frac{240}{24} = 10 \)

The values of \( k \) are all consistent (10, 10, 10), so this table **is** proportional with a constant of proportionality of 10.

### Conclusion:
The correct answer is:
**Choice C**

Would you like a detailed explanation of the process? Or do you have any specific questions?

Here are 5 related questions for further understanding:
1. How do you find the constant of proportionality from a graph?
2. Can a table have more than one constant of proportionality?
3. What would a table with a constant of proportionality of 5 look like?
4. How can you verify proportionality using equations instead of tables?
5. If \( y = 10x \), what is the value of \( y \) when \( x = 15 \)?

**Tip:** When checking for proportionality in a table, ensure that the ratio \( \frac{y}{x} \) is the same for all pairs.

Which table has a constant of proportionality between y and x of 10?

This problem teaches students how to find the constant of proportionality between y and x using tables. Includes step-by-step analysis and the key formula k = y / x. Suitable for Grades 6-8 math students.

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