Which table represents a proportional relationship that has a constant of proportionality equal to 0.8?

Question

A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 4, 8, 10. Column 2 is labeled y with entries 0, 0.5, 1, 1.25.
A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 5, 10, 12.5. Column 2 is labeled y with entries 0, 4, 8, 10.
A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 4, 8, 10. Column 2 is labeled y with entries 0.8, 0.8, 0.8, 0.8.
A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 5, 10, 12.5. Column 2 is labeled y with entries 0.8, 10.8, 20.8, 25.8.

Answer 1

To determine which table represents a proportional relationship with a constant of proportionality equal to 0.8, we want to find a relationship where \( y = kx \), where \( k = 0.8 \).

Let's analyze each option:

1. First Table:

   • x: 0, 4, 8, 10
   • y: 0, 0.5, 1, 1.25
   • To find k for each row:
     • For x = 4: k = 0.5/4 = 0.125
     • For x = 8: k = 1/8 = 0.125
     • For x = 10: k = 1.25/10 = 0.125
   • This table does not have a constant of proportionality of 0.8.

2. Second Table:

   • x: 0, 5, 10, 12.5
   • y: 0, 4, 8, 10
   • To find k for each row:
     • For x = 5: k = 4/5 = 0.8
     • For x = 10: k = 8/10 = 0.8
     • For x = 12.5: k = 10/12.5 = 0.8
   • This table has a constant of proportionality of 0.8.

3. Third Table:

   • x: 0, 4, 8, 10
   • y: 0.8, 0.8, 0.8, 0.8
   • Here, y is a constant value. This means that the relationship is not proportional as it does not depend on x.

4. Fourth Table:

   • x: 0, 5, 10, 12.5
   • y: 0.8, 10.8, 20.8, 25.8
   • To find k for each row:
     • For x = 5: k = 10.8/5 = 2.16
     • For x = 10: k = 20.8/10 = 2.08
     • For x = 12.5: k = 25.8/12.5 = 2.064
   • This table does not have a constant of proportionality of 0.8.

Thus, the correct table that represents a proportional relationship with a constant of proportionality equal to 0.8 is:

The second table.