Question

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

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

(2, 6)
Left Parenthesis 2 comma 6 Right Parenthesis

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

(2/3, 4)

Answer 1

Given that the amount of water is directly proportional to the number of cups of rice, we can express this relationship as:

water = k * rice

where k is the constant of proportionality. Since the coordinate (1/2, 1) is on the graph of this proportional relationship, we can find the constant k by plugging in the given values:

1 = k * (1/2)

To solve for k, multiply both sides by 2:

2 * 1 = k * (1/2) * 2
2 = k

Now we know that k = 2. This means that for every 1 cup of rice, we need 2 units of water. We can use this information to identify another point on the graph.

Let's test the given options:

A) (32, 3) - If we have 32 cups of rice, we would expect 32 * 2 = 64 units of water, not 3. This option does not fit the proportional relationship.

B) (3/2, 3) - If we have 3/2 cups of rice, we would expect (3/2) * 2 = 3 units of water. This option fits the proportional relationship.

C) (2, 6) - If we have 2 cups of rice, we would expect 2 * 2 = 4 units of water, not 6. This option does not fit the proportional relationship.

D) (1/4, 2) - If we have 1/4 cup of rice, we would expect (1/4) * 2 = 1/2 units of water, not 2. This option does not fit the proportional relationship.

E) (2/3, 4) - This option was not provided in the original list.

Therefore, based on the information provided, the correct option that fits the proportional relationship is:

B) (3/2, 3)