Which graph of ordered pairs shows a proportional relationship?

Question

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

Answer 1

To determine which set of ordered pairs shows a proportional relationship, we need to check if the ratio of \(y\) to \(x\) is constant for all points in each graph.

1. Points (−1, 2) and (2, −1):

   • For point (−1, 2): \( \frac{y}{x} = \frac{2}{-1} = -2 \)
   • For point (2, −1): \( \frac{y}{x} = \frac{-1}{2} = -0.5 \)
   • The ratios are not constant. Not proportional.

2. Points (−2, −3) and (2, 3):

   • For point (−2, −3): \( \frac{y}{x} = \frac{-3}{-2} = \frac{3}{2} \)
   • For point (2, 3): \( \frac{y}{x} = \frac{3}{2} \)
   • The ratios are constant. Proportional relationship.

3. Points (−2, −1) and (2, 3):

   • For point (−2, −1): \( \frac{y}{x} = \frac{-1}{-2} = \frac{1}{2} \)
   • For point (2, 3): \( \frac{y}{x} = \frac{3}{2} \)
   • The ratios are not constant. Not proportional.

4. Points (−1, 3) and (1, 1):

   • For point (−1, 3): \( \frac{y}{x} = \frac{3}{-1} = -3 \)
   • For point (1, 1): \( \frac{y}{x} = \frac{1}{1} = 1 \)
   • The ratios are not constant. Not proportional.

Based on the analysis, the second set of points (−2, −3) and (2, 3) shows a proportional relationship.