Question
Find if the following table represents a proportional relationship.
Ratio = 2, proportional
Ratio = 3, proportional
Ratio = 2, nonproportional
Ratio is not constant, nonproportional
Ratio = 2, proportional
Ratio = 3, proportional
Ratio = 2, nonproportional
Ratio is not constant, nonproportional
Answers
GPT-4o mini
To determine if the table represents a proportional relationship, we need to check if the ratios of corresponding values are constant throughout the entries.
A proportional relationship can be defined by the equation \( y = kx \), where \( k \) is a constant. In a proportional relationship, the ratio \( \frac{y}{x} \) must be the same for all pairs of \( x \) and \( y \).
From the information you provided:
1. Ratio = 2, proportional
2. Ratio = 3, proportional
3. Ratio = 2, nonproportional
4. Ratio is not constant, nonproportional
The first two entries suggest that we have some constant ratios (2 and 3) for some pairs but the third entry contradicts this by stating that ratio = 2 for those pairs is nonproportional.
The fourth entry states that "Ratio is not constant" which indicates that the ratios among the values change.
In conclusion, if some ratios are different (2, 3), and others are marked as nonproportional, it confirms that the overall table does not represent a proportional relationship.
Final determination: The table does **not** represent a proportional relationship, as the ratios are not constant.
A proportional relationship can be defined by the equation \( y = kx \), where \( k \) is a constant. In a proportional relationship, the ratio \( \frac{y}{x} \) must be the same for all pairs of \( x \) and \( y \).
From the information you provided:
1. Ratio = 2, proportional
2. Ratio = 3, proportional
3. Ratio = 2, nonproportional
4. Ratio is not constant, nonproportional
The first two entries suggest that we have some constant ratios (2 and 3) for some pairs but the third entry contradicts this by stating that ratio = 2 for those pairs is nonproportional.
The fourth entry states that "Ratio is not constant" which indicates that the ratios among the values change.
In conclusion, if some ratios are different (2, 3), and others are marked as nonproportional, it confirms that the overall table does not represent a proportional relationship.
Final determination: The table does **not** represent a proportional relationship, as the ratios are not constant.