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

(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

(2, 6)

Answer 1

To identify another point on the graph of the directly proportional relationship where the amount of water is proportional to the number of cups of rice, we can use the given point (1/2, 1) to find the constant of proportionality.

In a direct proportion, the relationship can be expressed as:

\[ y = kx \]

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

From the point (1/2, 1):

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

To find \( k \), we can rearrange the equation:

\[ k = 1 \cdot 2 = 2 \]

So the relationship can be expressed as:

\[ y = 2x \]

Now, let's check the given response options to see which point also satisfies this equation:

1. **(1/4, 2)**:
\[ y = 2 \cdot \frac{1}{4} = \frac{1}{2} \text{ (not valid)} \]

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

3. **(2/3, 4)**:
\[ y = 2 \cdot \frac{2}{3} = \frac{4}{3} \text{ (not valid)} \]

4. **(2, 6)**:
\[ y = 2 \cdot 2 = 4 \text{ (not valid)} \]

Thus, the point (3/2, 3) satisfies the proportional relationship \( y = 2x \). Therefore, another point on the graph is:

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