In a direct proportional relationship, if we have a point (x, y), then any other point on the graph can be found by multiplying both coordinates by the same factor.
The point (12, 1) indicates that for 12 cups of rice, there is 1 unit of water. The constant of proportionality \( k \) can be found as: \[ k = \frac{y}{x} = \frac{1}{12} \]
So, for any point (x, y), the relationship can be expressed as: \[ y = \frac{1}{12} x \]
To find another point, we can choose a different value for \( x \) and calculate \( y \): For \( x = 14 \): \[ y = \frac{1}{12} \cdot 14 = \frac{14}{12} = \frac{7}{6} \]
None of the provided points correspond to this. However, we can also check the provided options with different values:
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(32, 3): \[ 3 \neq \frac{32}{12} \Rightarrow 3 = \frac{8}{3} \text{ does not hold.} \]
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(2, 6): \[ 6 \neq \frac{2}{12} \Rightarrow 6 \text{ is not proportional to 2.} \]
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(23, 4): \[ 4 \neq \frac{23}{12} \Rightarrow 4 \text{ does not apply.} \]
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(14, 2): \[ 2 \neq \frac{14}{12} \Rightarrow 2 \text{ is not proportional to 14.} \]
No points match the proportional relationship found based on \( k = \frac{1}{12} \):
So, the answer is not among the provided points; however, if you were to choose one to simply test, (14, 2) would be the numerically closest, despite not matching the exact proportional relationship.
The correct proportional point could be any that you derive or calculate with the same scaling, such as (24, 2) for example.