To determine another point on the graph, we first need to understand the relationship described by the coordinates \( \left( \frac{1}{2}, 1 \right) \). This point suggests that for \( \frac{1}{2} \) cups of rice, there is \( 1 \) unit of water.
Since the relationship is directly proportional, we can express this relationship 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. Using the given point \( \left( \frac{1}{2}, 1 \right) \), we can find \( k \):
\[ 1 = k \left( \frac{1}{2} \right) \]
Multiplying both sides by 2 gives:
\[ k = 2 \]
Now the relationship can be expressed as:
\[ y = 2x \]
Using this equation, we can find another point by substituting a different value for \( x \). Let's evaluate the choices given:
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For \( \left( \frac{1}{4}, 2 \right) \): \[ y = 2 \left( \frac{1}{4} \right) = \frac{1}{2} \] (Not a valid point)
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For \( \left( \frac{3}{2}, 3 \right) \): \[ y = 2 \left( \frac{3}{2} \right) = 3 \] (This is a valid point)
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For \( \left( \frac{2}{3}, 4 \right) \): \[ y = 2 \left( \frac{2}{3} \right) = \frac{4}{3} \] (Not a valid point)
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For \( (2, 6) \): \[ y = 2(2) = 4 \] (Not a valid point)
The only valid option that maintains the proportional relationship is:
(3/2, 3)