Let's carefully analyze the table and the relationships between the amounts of rice and water:
| Amount of Rice (cups) | Amount of Water (cups) |
|-----------------------|------------------------|
| 2 | 5 |
| 3 | 7.5 |
| 5 | 12.5 |
| 8 | 20 |
1. Independent and Dependent Variables: In general, when examining relationships between two quantities, the independent variable is the one you have control over, and the dependent variable is the one that responds to changes in the independent variable.
2. Identification from the context: In cooking, the amount of water you need typically depends on, or is determined by, the amount of rice you are cooking.
- Here, you first decide the amount of rice you want to cook.
- Based on that decision, you then determine how much water is required.
3. Labeling the variables:
- The amount of rice is what you decide on first. Thus, it is the independent variable.
- The amount of water required depends on the amount of rice. Therefore, it is the dependent variable.
Based on this analysis:
- The statement "The amount of rice is the dependent value." is incorrect, because the amount of rice determines the amount of water, not the other way around.
- The statement "The amount of water is the dependent value." is correct, as the amount of water depends on the amount of rice.
- The statement "The amount of rice is the independent value." is correct, since the amount of rice is what you control first before determining the amount of water.
- The statement "The amount of water is the independent value." is incorrect, because the amount of water changes in response to the amount of rice, making it dependent.
- The statement "The values cannot be labeled as dependent or independent without a given equation." is incorrect. The independent and dependent variables can be identified based on the contextual relationship, even without a given equation.
Therefore, the two correct statements are:
- The amount of water is the dependent value.
- The amount of rice is the independent value.
