Which table has a constant of proportionality between
\[y\] and
\[x\] of

\[\dfrac{1}4\]?
Choose 1 answer:
Choose 1 answer:
(Choice A)
\[x\]
\[y\]
\[8\]
\[2\]
\[10\]
\[2.5\]
\[12\]
\[3\]

A
\[x\]
\[y\]
\[8\]
\[2\]
\[10\]
\[2.5\]
\[12\]
\[3\]
(Choice B)
\[x\]
\[y\]
\[3\]
\[1\]
\[6\]
\[2\]
\[9\]
\[3\]

B
\[x\]
\[y\]
\[3\]
\[1\]
\[6\]
\[2\]
\[9\]
\[3\]
(Choice C)
\[x\]
\[y\]
\[6\]
\[1.5\]
\[7\]
\[2\]
\[8\]
\[2.5\]

C
\[x\]
\[y\]
\[6\]
\[1.5\]
\[7\]
\[2\]
\[8\]
\[2.5\]

Do 13 problems

To find the table with a constant of proportionality of \(\frac{1}{4}\) between \(y\) and \(x\), we need to check if the ratio \(\frac{y}{x}\) is equal to \(\frac{1}{4}\) for all pairs of values in each table.

### Table A:
- For \(x = 8\) and \(y = 2\): \(\frac{y}{x} = \frac{2}{8} = \frac{1}{4}\)
- For \(x = 10\) and \(y = 2.5\): \(\frac{y}{x} = \frac{2.5}{10} = \frac{1}{4}\)
- For \(x = 12\) and \(y = 3\): \(\frac{y}{x} = \frac{3}{12} = \frac{1}{4}\)

### Table B:
- For \(x = 3\) and \(y = 1\): \(\frac{y}{x} = \frac{1}{3} \neq \frac{1}{4}\)
- For \(x = 6\) and \(y = 2\): \(\frac{y}{x} = \frac{2}{6} = \frac{1}{3} \neq \frac{1}{4}\)
- For \(x = 9\) and \(y = 3\): \(\frac{y}{x} = \frac{3}{9} = \frac{1}{3} \neq \frac{1}{4}\)

### Table C:
- For \(x = 6\) and \(y = 1.5\): \(\frac{y}{x} = \frac{1.5}{6} = \frac{1}{4}\)
- For \(x = 7\) and \(y = 2\): \(\frac{y}{x} = \frac{2}{7} \neq \frac{1}{4}\)
- For \(x = 8\) and \(y = 2.5\): \(\frac{y}{x} = \frac{2.5}{8} = \frac{5}{16} \neq \frac{1}{4}\)

**Conclusion:**
Table A has a constant of proportionality of \(\frac{1}{4}\) between \(y\) and \(x\).

**Correct Answer:** Choice A

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you determine if two variables are proportional?
2. Can the constant of proportionality be a fraction?
3. What happens if the ratio between \(y\) and \(x\) is not consistent?
4. How would you graph a relationship with a constant of proportionality of \(\frac{1}{4}\)?
5. How does the constant of proportionality relate to the slope of a line?

**Tip:** When working with proportional relationships, always ensure that the ratio between the two variables remains constant across all values.

Learn how to identify the table with a constant of proportionality of \(\frac{1}{4}\) between variables \(x\) and \(y\) using mathematical analysis. This problem demonstrates the application of proportional relationships in mathematics.

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