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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1 answer

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).