Since the amount of water is directly proportional to the number of cups of rice, we can express this relationship as:
\[ y = kx \]
where \( y \) is the amount of water, \( x \) 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 identify \( k \):
\[ 1 = k \left(\frac{1}{2}\right) \]
To solve for \( k \):
\[ k = 1 \div \frac{1}{2} = 2 \]
This means the relationship can be described by:
\[ y = 2x \]
Now we can identify another point on the graph by selecting a value for \( x \) and calculating \( y \).
- For \( x = 1 \):
\[ y = 2(1) = 2 \quad \Rightarrow \quad (1, 2) \]
- For \( x = 2 \):
\[ y = 2(2) = 4 \quad \Rightarrow \quad (2, 4) \]
- For \( x = 3 \):
\[ y = 2(3) = 6 \quad \Rightarrow \quad (3, 6) \]
Now let's check the options provided:
- \( \left( \frac{1}{4}, 2 \right) \) → This point doesn't fit as \( y \neq 2 \).
- \( \left( \frac{3}{2}, 3 \right) \) → \( y = 2 \left( \frac{3}{2} \right) = 3 \) (valid point).
- \( \left( \frac{2}{3}, 4 \right) \) → This point doesn't fit as \( y \neq 4 \).
- \( (2, 6) \) → This point doesn't fit as \( y \neq 6 \).
Thus, the correct option, which is also another point on the graph, is:
(3/2, 3)