The amount of water is directly proportional to the umber of cups of rice. The coordinate (1/2, 1) is on the graph of this proportional relationship. Identify another point of the graph.

A. (1/4, 2)
B. (2/3, 4)
C. (3/2, 3)
D. (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:

\[ y = kx \]

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

From the given point \((1/2, 1)\), we can determine \( k \):

\[ 1 = k \cdot \frac{1}{2} \]

Solving for \( k \):

\[ k = 1 \div \frac{1}{2} = 2 \]

Thus, the relationship can be described by the equation:

\[ y = 2x \]

Now we can use this equation to check each of the answer choices:

A. For \( (1/4, 2) \): \[ y = 2 \cdot \frac{1}{4} = \frac{2}{4} = \frac{1}{2} \quad \text{(not a valid point)} \]

B. For \( (2/3, 4) \): \[ y = 2 \cdot \frac{2}{3} = \frac{4}{3} \quad \text{(not a valid point)} \]

C. For \( (3/2, 3) \): \[ y = 2 \cdot \frac{3}{2} = 3 \quad \text{(this is a valid point)} \]

D. For \( (2, 6) \): \[ y = 2 \cdot 2 = 4 \quad \text{(not a valid point)} \]

Hence, the only valid point on the graph of this proportional relationship is:

C. (3/2, 3).