To find another point on the graph of a direct proportional relationship, we can use the information given by the coordinate (12, 1). This means that for 1 cup of rice, we need 12 units of water. Since the relationship is directly proportional, if we multiply the number of cups of rice by a constant factor, the amount of water will also be multiplied by the same factor.
The equation for direct proportionality can be stated 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 (12, 1), we can see that for 1 cup of rice (when \( x = 1 \)), the water amount is \[ k = \frac{y}{x} = \frac{12}{1} = 12 \]
So the equation for the relationship becomes: \[ y = 12x \]
Now let's check the given response options to see which one satisfies this equation:
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(2, 6): \[ y = 12(2) = 24 \] (not valid)
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(14, 2): \[ y = 12(14) = 168 \] (not valid)
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(32, 3): \[ y = 12(32) = 384 \] (not valid)
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(23, 4): \[ y = 12(23) = 276 \] (not valid)
None of the given points directly corresponds to the equation \( y = 12x\). However, you can also create your own points based on your understanding of the relationship.
For example, if you take \( x = 2 \), then: \[ y = 12(2) = 24 \] This point (2, 24) is a valid point on the graph, but is not in the response options provided.
Please check the response options to identify any inaccuracies or provide the necessary points that can be derived from (12, 1) using the established proportional relationship.