Given that the amount of water is directly proportional to the number of cups of rice, we can express this relationship as:
\[ W = kR \]
where:
- \( W \) is the amount of water,
- \( R \) is the number of cups of rice,
- \( k \) is the constant of proportionality.
The point \((1/2, 1)\) means that when \( R = 1/2 \), \( W = 1 \). We can use this point to find the constant \( k \):
\[ 1 = k \left(\frac{1}{2}\right) \] \[ k = 2 \]
Now, the relationship can be described as:
\[ W = 2R \]
Now we can use this equation to find another point on the graph by selecting a value for \( R \) and calculating the corresponding \( W \).
Let's examine the answer choices by evaluating each one to see if they fit the equation \( W = 2R \).
a) For \( R = 2 \): \[ W = 2(2) = 4 \] The point is \( (2, 4) \), which is not among the options.
b) For \( R = 3/2 \): \[ W = 2\left(\frac{3}{2}\right) = 3 \] The point is \( (3/2, 3) \), which is one of the options.
c) For \( R = 2/3 \): \[ W = 2\left(\frac{2}{3}\right) = \frac{4}{3} \] The point is \( (2/3, 4/3) \), which is not among the options.
d) For \( R = 1/4 \): \[ W = 2\left(\frac{1}{4}\right) = \frac{1}{2} \] The point is \( (1/4, 1/2) \), which is not among the options.
Based on this analysis, the point that lies on the graph of the proportional relationship is:
b) \( (3/2, 3) \).
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