Since the amount of water is directly proportional to the number of cups of rice, we can express this relationship 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 find \( k \):
\[ 1 = k \cdot 12 \] \[ k = \frac{1}{12} \]
This means the relationship can be described by:
\[ y = \frac{1}{12}x \]
To find another point on the graph, we can choose any value for \( x \) and calculate \( y \):
Let's calculate for \( x = 14 \):
\[ y = \frac{1}{12} \cdot 14 = \frac{14}{12} = \frac{7}{6} \]
This point (14, \( \frac{7}{6} \)) is not one of the options provided.
Now let's check each of the options given to see if they satisfy the equation \( y = \frac{1}{12}x \).
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(23, 4): \[ y = \frac{1}{12} \cdot 23 = \frac{23}{12} \] (not equal to 4)
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(2, 6): \[ y = \frac{1}{12} \cdot 2 = \frac{2}{12} = \frac{1}{6} \] (not equal to 6)
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(32, 3): \[ y = \frac{1}{12} \cdot 32 = \frac{32}{12} = \frac{8}{3} \] (not equal to 3)
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(14, 2): \[ y = \frac{1}{12} \cdot 14 = \frac{14}{12} = \frac{7}{6} \] (not equal to 2)
It looks like none of the given points are correct according to the proportional relationship derived from the point (12, 1). However, it could be possible to find a simple correct point by choosing another integer value.
Since the options do not match, the finding of another point based on the established \( k \) yields:
A valid point could be \( (0, 0) \) or if we look for simple multiples like \( (12, 1) \to (24, 2) \) based on \( k \) which yields a known relationship already.
If you want a suggestion, the point (24, 2) is also valid for this relationship since it maintains the ratio. However, it’s not listed. Please verify the task constraints as per allowed values.
14 answers