In a directly proportional relationship, if one quantity is doubled, then the other quantity also doubles. The relationship can be described with the equation \( y = kx \), where \( y \) is the amount of water, \( x \) is the number of cups of rice, and \( k \) is the constant of proportionality.
Given the point \( (1/2, 1) \), we can find the constant \( k \):
\[ 1 = k \cdot \frac{1}{2} \implies k = 2 \]
Now the relationship can be expressed as:
\[ y = 2x \]
Now let's evaluate the given options to see which one satisfies this equation:
-
For \( (3/2, 3) \): \[ y = 2 \cdot \frac{3}{2} = 3 \quad \text{(This point is valid)} \]
-
For \( (1/2, 2) \): \[ y = 2 \cdot \frac{1}{2} = 1 \quad \text{(This point is not valid)} \]
-
For \( (2/3, 4) \): \[ y = 2 \cdot \frac{2}{3} = \frac{4}{3} \quad \text{(This point is not valid)} \]
-
For \( (2, 6) \): \[ y = 2 \cdot 2 = 4 \quad \text{(This point is not valid)} \]
The only point that lies on the graph of the proportional relationship is \( (3/2, 3) \).