Question

You can use the Desmos Graphing Calculator to help solve this problem. Which sets represent proportional relationships? Select the two that apply.(2 points)Responses(1.5, 3), (4, 6), (4, 8)(1.5, 3), (4, 6), (4, 8)(3, 1), (6, 2), (9, 3)(3, 1), (6, 2), (9, 3)(3, 1), (4, 3), (8, 6)(3, 1), (4, 3), (8, 6)(2, 4), (4, 6), (7, 9)(2, 4), (4, 6), (7, 9)

Answer 1

To determine which sets represent proportional relationships, we need to identify the sets of points where the ratio of \( y \) to \( x \) is constant.

1. Set (1.5, 3), (4, 6), (4, 8):

   • Ratios:
     • \( \frac{3}{1.5} = 2 \)
     • \( \frac{6}{4} = 1.5 \)
     • \( \frac{8}{4} = 2 \)
   • This set does not represent a proportional relationship because the ratios are not the same.

2. Set (3, 1), (6, 2), (9, 3):

   • Ratios:
     • \( \frac{1}{3} = \frac{1}{3} \)
     • \( \frac{2}{6} = \frac{1}{3} \)
     • \( \frac{3}{9} = \frac{1}{3} \)
   • This set represents a proportional relationship, as all ratios are equal.

3. Set (3, 1), (4, 3), (8, 6):

   • Ratios:
     • \( \frac{1}{3} \)
     • \( \frac{3}{4} = 0.75 \)
     • \( \frac{6}{8} = 0.75 \)
   • This set does not represent a proportional relationship because the ratios are not the same.

4. Set (2, 4), (4, 6), (7, 9):

   • Ratios:
     • \( \frac{4}{2} = 2 \)
     • \( \frac{6}{4} = 1.5 \)
     • \( \frac{9}{7} \approx 1.2857 \)
   • This set does not represent a proportional relationship because the ratios are not the same.

Thus, the only set that represents a proportional relationship is:

• (3, 1), (6, 2), (9, 3)

In summary, the two options that apply as proportional relationships are:

1. (3, 1), (6, 2), (9, 3)
2. There are no other proportional relationships from the given options.