Given that the amount of water is directly proportional to the number of cups of rice, we can express this relationship mathematically 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 \( \left(\frac{1}{2}, 1\right) \), we can substitute into the equation to find \( k \):
\[ 1 = k \cdot \frac{1}{2} \] \[ k = 2 \]
Now that we have \( k \), we can write the equation for the proportionality:
\[ W = 2R \]
To find another point on this graph, we can check each of the given options by plugging the \( R \) values into the equation \( W = 2R \) and see if they provide a corresponding \( W \) value.
A. For \( R = 2 \): \[ W = 2 \cdot 2 = 4 \] Resulting point: \( (2, 4) \) (not included in the options)
B. For \( R = \frac{2}{3} \): \[ W = 2 \cdot \frac{2}{3} = \frac{4}{3} \] Resulting point: \( \left(\frac{2}{3}, \frac{4}{3}\right) \) (not included in the options)
C. For \( R = \frac{1}{4} \): \[ W = 2 \cdot \frac{1}{4} = \frac{1}{2} \] Resulting point: \( \left(\frac{1}{4}, \frac{1}{2}\right) \) (not included in the options)
D. For \( R = \frac{3}{2} \): \[ W = 2 \cdot \frac{3}{2} = 3 \] Resulting point: \( \left(\frac{3}{2}, 3\right) \) (this matches option D)
Thus, the correct answer is:
D. \( \left(\frac{3}{2}, 3\right) \)