Which graph shows a proportional relationship?

Question

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

Answer 1

A proportional relationship between two quantities can be identified if the ratio of the two quantities is constant. This means that if you plot the points on a coordinate plane, the graph of the points should form a straight line that passes through the origin (0,0).

Let's analyze the four sets of points:

1. Points (2, 3), (3, 8), and (6, 9):

   • The ratios are not consistent; for example, 3/2 ≠ 8/3 ≠ 9/6. Thus, this is not a proportional relationship.

2. Points (2, 4), (3, 6), and (5, 10):

   • The ratios are:
     • 4/2 = 2
     • 6/3 = 2
     • 10/5 = 2
   • Since all ratios are equal (2), this set of points shows a proportional relationship.

3. Points (1, 3), (4, 4), and (5, 10):

   • The ratios are:
     • 3/1 = 3
     • 4/4 = 1
     • 10/5 = 2
   • These ratios are not consistent. Thus, this is not a proportional relationship.

4. Points (2, 9), (5, 4), and (9, 3):

   • The ratios are not consistent; for example, 9/2 ≠ 4/5 ≠ 3/9. Thus, this is not a proportional relationship.

The only graph that shows a proportional relationship is the one with the points (2, 4), (3, 6), and (5, 10).