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

Since the amount of water is directly proportional to the number of cups of rice, we can express this relationship 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 \( \left(\frac{1}{2}, 1\right) \), we can identify \( k \):

\[
1 = k \left(\frac{1}{2}\right)
\]

To solve for \( k \):

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

This means the relationship can be described by:

\[
y = 2x
\]

Now we can identify another point on the graph by selecting a value for \( x \) and calculating \( y \).

1. For \( x = 1 \):

\[
y = 2(1) = 2 \quad \Rightarrow \quad (1, 2)
\]

2. For \( x = 2 \):

\[
y = 2(2) = 4 \quad \Rightarrow \quad (2, 4)
\]

3. For \( x = 3 \):

\[
y = 2(3) = 6 \quad \Rightarrow \quad (3, 6)
\]

Now let's check the options provided:

- \( \left( \frac{1}{4}, 2 \right) \) → This point doesn't fit as \( y \neq 2 \).
- \( \left( \frac{3}{2}, 3 \right) \) → \( y = 2 \left( \frac{3}{2} \right) = 3 \) (valid point).
- \( \left( \frac{2}{3}, 4 \right) \) → This point doesn't fit as \( y \neq 4 \).
- \( (2, 6) \) → This point doesn't fit as \( y \neq 6 \).

Thus, the correct option, which is also another point on the graph, is:

**(3/2, 3)**