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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.

1 answer

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.