To find another point on the graph of the direct proportionality between the amount of water and the number of cups of rice, we can use the point (1/2, 1) that you provided.
The direct proportionality relationship can be expressed as \( y = kx \), where \( k \) is the constant of proportionality.
From the point (1/2, 1):
- When \( x = 1/2 \), \( y = 1 \).
To find \( k \): \[ 1 = k \cdot \frac{1}{2} \] \[ k = 2 \]
Now we have the equation: \[ y = 2x \]
Now, we can find the coordinates of another point using this equation. For example, if we choose \( x = 2 \): \[ y = 2 \cdot 2 = 4 \] So, the point (2, 4) is on the graph.
Now let's evaluate the provided options:
- (23, 4)
- (2/3, 4)
- (2, 6)
- (3/2, 3)
- (1/4, 2)
We can check each option using the equation \( y = 2x \):
- For (23, 4): \( 4 \neq 2 \cdot 23 \) (not a valid point).
- For (2/3, 4): \( 4 \neq 2 \cdot \frac{2}{3} = \frac{4}{3} \) (not a valid point).
- For (2, 6): \( 6 \neq 2 \cdot 2 = 4 \) (not a valid point).
- For (3/2, 3): \( 3 \neq 2 \cdot \frac{3}{2} = 3 \) (valid point).
- For (1/4, 2): \( 2 \neq 2 \cdot \frac{1}{4} = \frac{1}{2} \) (not a valid point).
The only valid point from the provided responses that lies on the graph is:
(3/2, 3).
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