Question

Which table of ordered pairs represents a proportional relationship?
A 2-column table with 3 rows. Column 1 is labeled x with entries negative 3, negative 4, negative 5. Column 2 is labeled y with entries 3, 2, 1.
A 2-column table with 3 rows. Column 1 is labeled x with entries negative 1, negative 3, negative 5. Column 2 is labeled y with entries 1, 3, 5.
A 2-column table with 3 rows. Column 1 is labeled x with entries negative 2, negative 4, negative 6. Column 2 is labeled y with entries negative 5, negative 7, negative 9.
A 2-column table with 3 rows. Column 1 is labeled x with entries negative 2, negative 3, negative 4. Column 2 is labeled y with entries 0, negative 1, negative 2.

Answer 1

To determine which table of ordered pairs represents a proportional relationship, we need to check if the ratios \( \frac{y}{x} \) are constant for each pair of values in each table.

1. **First table**:
- \((-3, 3) \Rightarrow \frac{3}{-3} = -1\)
- \((-4, 2) \Rightarrow \frac{2}{-4} = -\frac{1}{2}\)
- \((-5, 1) \Rightarrow \frac{1}{-5} = -\frac{1}{5}\)

The ratios are not constant. So, this is not a proportional relationship.

2. **Second table**:
- \((-1, 1) \Rightarrow \frac{1}{-1} = -1\)
- \((-3, 3) \Rightarrow \frac{3}{-3} = -1\)
- \((-5, 5) \Rightarrow \frac{5}{-5} = -1\)

The ratios are constant at -1. So, this is a proportional relationship.

3. **Third table**:
- \((-2, -5) \Rightarrow \frac{-5}{-2} = \frac{5}{2}\)
- \((-4, -7) \Rightarrow \frac{-7}{-4} = \frac{7}{4}\)
- \((-6, -9) \Rightarrow \frac{-9}{-6} = \frac{3}{2}\)

The ratios are not constant. So, this is not a proportional relationship.

4. **Fourth table**:
- \((-2, 0) \Rightarrow \frac{0}{-2} = 0\)
- \((-3, -1) \Rightarrow \frac{-1}{-3} = \frac{1}{3}\)
- \((-4, -2) \Rightarrow \frac{-2}{-4} = \frac{1}{2}\)

The ratios are not constant. So, this is not a proportional relationship.

**Conclusion**: The second table represents a proportional relationship.