Which table of ordered pairs represents a proportional relationship?

Question

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 4, 16, 36.
A 2-column table with 3 rows. Column 1 is labeled x with entries negative 4, negative 6, negative 8. Column 2 is labeled y with entries negative 8, negative 12, negative 18.
A 2-column table with 3 rows. Column 1 is labeled x with entries negative 3, negative 5, negative 7. Column 2 is labeled y with entries 5, 3, 1.
A 2-column table with 3 rows. Column 1 is labeled x with entries negative 3, negative 6, negative 9. Column 2 is labeled y with entries 12, 24, 36.

Answer 1

To determine which table of ordered pairs represents a proportional relationship, we need to check if the ratio of \( y \) to \( x \) (i.e., \(\frac{y}{x}\)) is constant for all entries in the table.

1. First table (x: -2, -4, -6; y: 4, 16, 36):

   • \(\frac{4}{-2} = -2\)
   • \(\frac{16}{-4} = -4\)
   • \(\frac{36}{-6} = -6\)
   • Ratios are not constant.

2. Second table (x: -4, -6, -8; y: -8, -12, -18):

   • \(\frac{-8}{-4} = 2\)
   • \(\frac{-12}{-6} = 2\)
   • \(\frac{-18}{-8} = 2.25\)
   • Ratios are not constant.

3. Third table (x: -3, -5, -7; y: 5, 3, 1):

   • \(\frac{5}{-3} \approx -1.67\)
   • \(\frac{3}{-5} = -0.6\)
   • \(\frac{1}{-7} \approx -0.14\)
   • Ratios are not constant.

4. Fourth table (x: -3, -6, -9; y: 12, 24, 36):

   • \(\frac{12}{-3} = -4\)
   • \(\frac{24}{-6} = -4\)
   • \(\frac{36}{-9} = -4\)
   • Ratios are constant.

Thus, the table that represents a proportional relationship is the fourth table:

• x: -3, -6, -9
• y: 12, 24, 36