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

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

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

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

(3/2, 3)
Left Parenthesis Start Fraction 3 over 2 End Fraction comma 3 Right Parenthesis
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page 13 of 13

Answer 1

To identify another point on the graph of the given proportional relationship, we need to determine the constant of proportionality (k) based on the provided point (1/2, 1).

In a direct proportionality, we have:

\[ y = kx \]

Here, \( x \) is the number of cups of rice, and \( y \) is the amount of water. With the point \( (1/2, 1) \):

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

Solving for \( k \):

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

So the relationship can be expressed as:

\[ y = 2x \]

Now, we can find another point by choosing a different value for \( x \).

Let's check the provided options:

1. **(1/4, 2)**
For \( x = 1/4 \):
\( y = 2 \cdot \frac{1}{4} = \frac{1}{2} \) (not equal to 2)

2. **(2, 6)**
For \( x = 2 \):
\( y = 2 \cdot 2 = 4 \) (not equal to 6)

3. **(2/3, 4)**
For \( x = 2/3 \):
\( y = 2 \cdot \frac{2}{3} = \frac{4}{3} \) (not equal to 4)

4. **(3/2, 3)**
For \( x = 3/2 \):
\( y = 2 \cdot \frac{3}{2} = 3 \) (this point works!)

Thus, the correct response is:

**(3/2, 3)**.