Since the amount of water is directly proportional to the number of cups of ice, we can express this relationship mathematically as:
\[ W = k \cdot I \]
where \( W \) is the amount of water, \( I \) is the number of cups of ice, and \( k \) is the constant of proportionality.
Given the point \((\frac{1}{2}, 1)\), we can identify that with 1 cup of ice (i.e., \( I = 1 \)), the amount of water is \( W = k \cdot \frac{1}{2} \). Therefore, we can find \( k \) by plugging in these values.
From the point \((\frac{1}{2}, 1)\):
\[ 1 = k \cdot \frac{1}{2} \implies k = 2 \]
Thus, the relationship becomes:
\[ W = 2 \cdot I \]
Now we can verify which of the given points lies on this line, meaning the coordinates \((I, W)\) satisfy the equation \( W = 2 \cdot I \).
Let's check each option:
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A: \((\frac{2}{3}, 4)\)
\[ W = 2 \cdot \frac{2}{3} = \frac{4}{3} \quad \text{(not equal to 4)}\]
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B: \((2, 6)\)
\[ W = 2 \cdot 2 = 4 \quad \text{(not equal to 6)}\]
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C: \((\frac{3}{2}, 3)\)
\[ W = 2 \cdot \frac{3}{2} = 3 \quad \text{(equal to 3)}\]
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D: \((\frac{1}{4}, 2)\)
\[ W = 2 \cdot \frac{1}{4} = \frac{1}{2} \quad \text{(not equal to 2)}\]
The point that satisfies the equation \( W = 2 \cdot I \) is C: \((\frac{3}{2}, 3)\).
So, another point on the graph is \( \left(\frac{3}{2}, 3\right) \).
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