Question

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

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

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

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

(1/4, 2)

Answer 1

To solve the problem, we need to understand that the relationship between the amount of water and the number of cups of rice is directly proportional. This means we can express it 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 coordinate (1/2, 1), we can determine the value of \( k \):

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

Now, we can write the equation of the proportional relationship as:

\[ y = 2x \]

We can use this equation to find another point on the graph by choosing a value for \( x \) and calculating the corresponding \( y \).

Let's check each response:

1. **(2, 6)**:
\[ y = 2(2) = 4 \quad \text{(not valid, output is 4, not 6)} \]

2. **(3/2, 3)**:
\[ y = 2\left(\frac{3}{2}\right) = 3 \quad \text{(valid)} \]

3. **(2/3, 4)**:
\[ y = 2\left(\frac{2}{3}\right) = \frac{4}{3} \quad \text{(not valid, output is 4/3, not 4)} \]

4. **(1/4, 2)**:
\[ y = 2\left(\frac{1}{4}\right) = \frac{1}{2} \quad \text{(not valid, output is 1/2, not 2)} \]

The only valid point from the options given is:

**(3/2, 3)**

So, the answer is **(3/2, 3)**.