Question
Select all tables that represent a proportional relationship between x and y.
A
x 0 1 2 3
y 3 6 9 12
B
x 2 3 4 5
y 12 18 24 30
C
x 2 4 6 9
y 0 2 4 6
D
x 0 1 2 3
y 0 2 5 9
Answers
GPT-4o mini
To determine which tables represent a proportional relationship between \( x \) and \( y \), we need to check if the ratio \( \frac{y}{x} \) is constant for all values of \( x \) (excluding \( x = 0 \) where \( y \) should be \( 0 \)).
Let's analyze each table:
**Table A:**
- \( x = 1, y = 6 \Rightarrow \frac{y}{x} = \frac{6}{1} = 6 \)
- \( x = 2, y = 9 \Rightarrow \frac{y}{x} = \frac{9}{2} = 4.5 \)
- \( x = 3, y = 12 \Rightarrow \frac{y}{x} = \frac{12}{3} = 4 \)
**Conclusion:** The ratios are not constant. Not proportional.
---
**Table B:**
- \( x = 2, y = 12 \Rightarrow \frac{y}{x} = \frac{12}{2} = 6 \)
- \( x = 3, y = 18 \Rightarrow \frac{y}{x} = \frac{18}{3} = 6 \)
- \( x = 4, y = 24 \Rightarrow \frac{y}{x} = \frac{24}{4} = 6 \)
- \( x = 5, y = 30 \Rightarrow \frac{y}{x} = \frac{30}{5} = 6 \)
**Conclusion:** The ratios are constant at 6. This is proportional.
---
**Table C:**
- \( x = 2, y = 0 \Rightarrow \frac{y}{x} = \frac{0}{2} = 0 \)
- \( x = 4, y = 2 \Rightarrow \frac{y}{x} = \frac{2}{4} = 0.5 \)
- \( x = 6, y = 4 \Rightarrow \frac{y}{x} = \frac{4}{6} \approx 0.67 \)
- \( x = 9, y = 6 \Rightarrow \frac{y}{x} = \frac{6}{9} \approx 0.67 \)
**Conclusion:** The ratios are not constant. Not proportional.
---
**Table D:**
- \( x = 1, y = 2 \Rightarrow \frac{y}{x} = \frac{2}{1} = 2 \)
- \( x = 2, y = 5 \Rightarrow \frac{y}{x} = \frac{5}{2} = 2.5 \)
- \( x = 3, y = 9 \Rightarrow \frac{y}{x} = \frac{9}{3} = 3 \)
**Conclusion:** The ratios are not constant. Not proportional.
---
### Final Answer:
The only table that represents a proportional relationship between \( x \) and \( y \) is:
**B**
Let's analyze each table:
**Table A:**
- \( x = 1, y = 6 \Rightarrow \frac{y}{x} = \frac{6}{1} = 6 \)
- \( x = 2, y = 9 \Rightarrow \frac{y}{x} = \frac{9}{2} = 4.5 \)
- \( x = 3, y = 12 \Rightarrow \frac{y}{x} = \frac{12}{3} = 4 \)
**Conclusion:** The ratios are not constant. Not proportional.
---
**Table B:**
- \( x = 2, y = 12 \Rightarrow \frac{y}{x} = \frac{12}{2} = 6 \)
- \( x = 3, y = 18 \Rightarrow \frac{y}{x} = \frac{18}{3} = 6 \)
- \( x = 4, y = 24 \Rightarrow \frac{y}{x} = \frac{24}{4} = 6 \)
- \( x = 5, y = 30 \Rightarrow \frac{y}{x} = \frac{30}{5} = 6 \)
**Conclusion:** The ratios are constant at 6. This is proportional.
---
**Table C:**
- \( x = 2, y = 0 \Rightarrow \frac{y}{x} = \frac{0}{2} = 0 \)
- \( x = 4, y = 2 \Rightarrow \frac{y}{x} = \frac{2}{4} = 0.5 \)
- \( x = 6, y = 4 \Rightarrow \frac{y}{x} = \frac{4}{6} \approx 0.67 \)
- \( x = 9, y = 6 \Rightarrow \frac{y}{x} = \frac{6}{9} \approx 0.67 \)
**Conclusion:** The ratios are not constant. Not proportional.
---
**Table D:**
- \( x = 1, y = 2 \Rightarrow \frac{y}{x} = \frac{2}{1} = 2 \)
- \( x = 2, y = 5 \Rightarrow \frac{y}{x} = \frac{5}{2} = 2.5 \)
- \( x = 3, y = 9 \Rightarrow \frac{y}{x} = \frac{9}{3} = 3 \)
**Conclusion:** The ratios are not constant. Not proportional.
---
### Final Answer:
The only table that represents a proportional relationship between \( x \) and \( y \) is:
**B**