Which graph of ordered pairs shows a proportional relationship?

Question

On a coordinate plane, points (1, negative 2) and (2, negative 4) are plotted.
On a coordinate plane, points (negative 2, negative 2) and (1, 3) are plotted.
On a coordinate plane, points (negative 2, 1) and (1, negative 2) are plotted.
On a coordinate plane, points (2, 1) and (4, 3) are plotted.

Answer 1

To determine which graph shows a proportional relationship among the given sets of ordered pairs, we need to check if the ratio of the y-coordinates to the x-coordinates is constant for each point.

1. For the points (1, -2) and (2, -4):

   • For (1, -2): \(\frac{-2}{1} = -2\)
   • For (2, -4): \(\frac{-4}{2} = -2\)
   • The ratios are the same, so this set shows a proportional relationship.

2. For the points (-2, -2) and (1, 3):

   • For (-2, -2): \(\frac{-2}{-2} = 1\)
   • For (1, 3): \(\frac{3}{1} = 3\)
   • The ratios are different, so this set does not show a proportional relationship.

3. For the points (-2, 1) and (1, -2):

   • For (-2, 1): \(\frac{1}{-2} = -0.5\)
   • For (1, -2): \(\frac{-2}{1} = -2\)
   • The ratios are different, so this set does not show a proportional relationship.

4. For the points (2, 1) and (4, 3):

   • For (2, 1): \(\frac{1}{2} = 0.5\)
   • For (4, 3): \(\frac{3}{4} = 0.75\)
   • The ratios are different, so this set does not show a proportional relationship.

Therefore, the only set of ordered pairs that shows a proportional relationship is the first one: (1, -2) and (2, -4).