Bot GPT 4-o mini The given point (12, 1) indicates that for 12 cups of rice, the amount of water is 1 unit (let's say 1 cup for easier understanding). Since the amount of water is directly proportional to the number of cups of rice, we can express the relationship as \( W = kR \), where \( W \) is the amount of water, \( R \) is the number of cups of rice, and \( k \) is the constant of proportionality.
From the point (12, 1), we can find \( k \) as follows: \[ k = \frac{W}{R} = \frac{1}{12} \]
This means that the amount of water for any number of cups of rice can be calculated using: \[ W = \frac{1}{12} R \]
Now, we need to find another point on the graph. We can select a different value for \( R \) and calculate \( W \).
Let's try \( R = 24 \): \[ W = \frac{1}{12} \times 24 = 2 \]
This gives us the point (24, 2).
Now, let's check the provided responses:
- (14, 2) - Using the formula, \( W = \frac{1}{12} \times 14 \neq 2 \).
- (23, 4) - Using the formula, \( W = \frac{1}{12} \times 23 \neq 4 \).
- (32, 3) - Using the formula, \( W = \frac{1}{12} \times 32 \neq 3 \).
- (2, 6) - Using the formula, \( W = \frac{1}{12} \times 2 \neq 6 \).
None of the provided responses accurately reflects a point on the graph if we consider the formula derived from the initial point (12, 1).
The correct point we derived, (24, 2), is not listed among the responses. Thus, it seems that none of the options provided is valid based on the proportional relationship established.
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