Since the amount of water is directly proportional to the number of cups of rice, we can express this relationship as:
\[ k = \frac{w}{r} \]
where \( k \) is the constant of proportionality, \( w \) is the amount of water, and \( r \) is the number of cups of rice.
Given the point (12, 1), this means that when there are 12 cups of rice, there is 1 unit of water. We can calculate the constant of proportionality \( k \):
\[ k = \frac{1}{12} \]
Now, using this constant \( k \), we can find another point on the graph by picking a different value for \( r \) (the number of cups of rice):
Let’s consider the relationship:
\[ w = k \cdot r \] \[ w = \frac{1}{12} \cdot r \]
Now, if we consider \( r = 2 \):
\[ w = \frac{1}{12} \cdot 2 = \frac{1}{6} \]
Thus, the point (2, 1/6) is on the graph. However, this specific point is not one of the responses provided.
Next, let's evaluate the given response options:
- (2, 6)
- (23, 4)
- (32, 3)
- (14, 2)
We need to check each point to see if it maintains the proportionality:
For (2, 6):
- Using \( k = \frac{w}{r} \) gives \( k = \frac{6}{2} = 3 \) (not consistent with \( k = \frac{1}{12} \)).
For (23, 4):
- \( k = \frac{4}{23} \) (not consistent).
For (32, 3):
- \( k = \frac{3}{32} \) (not consistent).
For (14, 2):
- \( k = \frac{2}{14} = \frac{1}{7} \) (not consistent).
None of the provided points seem to be consistent with the original point (12, 1).
However, if we double the original point (12, 1) (multiply both coordinates by 2), we get (24, 2).
Since we cannot create a point from the options given based on the existing proportional relationships, we need to check which of these might be the closest based on scaling, but none align properly.
Would you like to try different scaling factors? Or can any clarification on the points be provided?