Question
Which table represents a proportional relationship that has a constant of proportionality equal to 0.8?
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.
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.
Answers
GPT-4o mini
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.**
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.**