To identify another point on the graph of the given proportional relationship, we need to determine the constant of proportionality (k) based on the provided point (1/2, 1).
In a direct proportionality, we have:
\[ y = kx \]
Here, \( x \) is the number of cups of rice, and \( y \) is the amount of water. With the point \( (1/2, 1) \):
\[ 1 = k \cdot \frac{1}{2} \]
Solving for \( k \):
\[ k = 1 \div \frac{1}{2} = 2 \]
So the relationship can be expressed as:
\[ y = 2x \]
Now, we can find another point by choosing a different value for \( x \).
Let's check the provided options:
-
(1/4, 2)
For \( x = 1/4 \):
\( y = 2 \cdot \frac{1}{4} = \frac{1}{2} \) (not equal to 2) -
(2, 6)
For \( x = 2 \):
\( y = 2 \cdot 2 = 4 \) (not equal to 6) -
(2/3, 4)
For \( x = 2/3 \):
\( y = 2 \cdot \frac{2}{3} = \frac{4}{3} \) (not equal to 4) -
(3/2, 3)
For \( x = 3/2 \):
\( y = 2 \cdot \frac{3}{2} = 3 \) (this point works!)
Thus, the correct response is:
(3/2, 3).