The amount of water is directly proportional to the number of cups of rice. The coordinate (12, 1)

is on the graph of this proportional relationship. Identify another point on the graph.(1 point)
Responses

(14, 2)
Left Parenthesis Start Fraction 1 over 4 End Fraction comma 2 Right Parenthesis

(23, 4)
Left Parenthesis Start Fraction 2 over 3 End Fraction comma 4 Right Parenthesis

(32, 3)
Left Parenthesis Start Fraction 3 over 2 End Fraction comma 3 Right Parenthesis

(2, 6)

1 answer

Since the amount of water is directly proportional to the number of cups of rice, we can express this relationship with the equation:

\[ W = kR \]

where \( W \) is the amount of water, \( R \) is the number of cups of rice, and \( k \) is the constant of proportionality.

From the point (12, 1), we can find \( k \):

\[ 1 = k \cdot 12 \]

Solving for \( k \):

\[ k = \frac{1}{12} \]

Now, using this constant \( k \), we can find other points on the graph. For any value of \( R \), we can calculate \( W \) using:

\[ W = \frac{1}{12}R \]

Let's check each of the provided options to see which one maintains the proportionality:

  1. For (14, 2): \[ W = \frac{1}{12} \cdot 14 = \frac{14}{12} = \frac{7}{6} \] (not equal to 2)

  2. For (23, 4): \[ W = \frac{1}{12} \cdot 23 = \frac{23}{12} \] (not equal to 4)

  3. For (32, 3): \[ W = \frac{1}{12} \cdot 32 = \frac{32}{12} = \frac{8}{3} \] (not equal to 3)

  4. For (2, 6): \[ W = \frac{1}{12} \cdot 2 = \frac{2}{12} = \frac{1}{6} \] (not equal to 6)

None of the provided alternatives appear to provide a valid point for \( W \) in accordance with the given proportional relationship.

For additional context, you can find another valid point using the derived formula. If you try \( R = 6 \):

\[ W = \frac{1}{12} \cdot 6 = \frac{1}{2} \]

thus (6, 0.5) would be a valid point. However, assuming you need the options you provided, none of these options are correct. Consider checking the problem or recalculating possible responses for further confirmation.