Which graph shows a proportional relationship?

Question

1.On a coordinate plane, points (2, 3), (3, 8), and (6, 9) are plotted.
2.On a coordinate plane, points (2, 4), (3, 6), and (5, 10) are plotted.
3.On a coordinate plane, points (1, 3), (4, 4), and (5, 10) are plotted.
4.On a coordinate plane, points (2, 9), (5, 4), and (9, 3) are plotted.

Answer 1

A proportional relationship between two variables is characterized by a constant ratio between them, which means that the graph of the relationship will be a straight line passing through the origin (0,0).

To identify which set of points shows a proportional relationship, we can examine the ratios (y/x) for each point.

1. For points (2, 3), (3, 8), (6, 9):

   • (2, 3): 3/2 = 1.5
   • (3, 8): 8/3 ≈ 2.67
   • (6, 9): 9/6 = 1.5
   • Not proportional (different ratios).

2. For points (2, 4), (3, 6), (5, 10):

   • (2, 4): 4/2 = 2
   • (3, 6): 6/3 = 2
   • (5, 10): 10/5 = 2
   • Proportional (all ratios are equal).

3. For points (1, 3), (4, 4), (5, 10):

   • (1, 3): 3/1 = 3
   • (4, 4): 4/4 = 1
   • (5, 10): 10/5 = 2
   • Not proportional (different ratios).

4. For points (2, 9), (5, 4), (9, 3):

   • (2, 9): 9/2 = 4.5
   • (5, 4): 4/5 = 0.8
   • (9, 3): 3/9 = 0.33
   • Not proportional (different ratios).

Thus, the only graph that shows a proportional relationship is option 2.