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.
A: (2, 6)
B: (3/2, 3)
C: (1/4, 2)
D: (2/3, 4)
To identify another point on the graph, we can use the concept of direct proportionality.
Given that the amount of water is directly proportional to the number of cups of rice, we can set up a proportion using the given point (1/2, 1) and another point (x, y) on the graph.
The proportion is: 1/2 : 1 = x : y
Cross multiplying, we have 2x = y.
Now we can check which of the given points satisfies this relationship:
A: (2, 6) -> 2(2) = 6 (not satisfied)
B: (3/2, 3) -> 2(3/2) = 3 (satisfied)
C: (1/4, 2) -> 2(1/4) = 1/2 (not satisfied)
D: (2/3, 4) -> 2(2/3) = 4/3 (not satisfied)
Therefore, the point (3/2, 3) satisfies the relationship, so the correct answer is B: (3/2, 3).
To identify another point on the graph of this proportional relationship, we can use the same proportionality constant (also known as the constant of variation) between water and cups of rice.
Given that the amount of water is directly proportional to the number of cups of rice, we can express this relationship using the equation:
water = k * rice,
where k is the proportionality constant.
From the given coordinate (1/2, 1), we can substitute these values into the equation:
1 = k * (1/2).
Simplifying the equation, we have:
1 = k/2,
2 = k.
Now that we have found the value of the proportionality constant, we can use it to find another point on the graph.
Let's substitute the constant k = 2 into each of the answer choices:
A: (2, 6) -> water = 2 * 2 = 4 (Not equal to 6)
B: (3/2, 3) -> water = 2 * (3/2) = 3 (Equal to 3)
C: (1/4, 2) -> water = 2 * (1/4) = 1/2 (Not equal to 2)
D: (2/3, 4) -> water = 2 * (2/3) = 4/3 (Not equal to 4)
From this analysis, we can see that the only point that satisfies the proportional relationship is B: (3/2, 3).
To identify another point on the graph, we can use the given information that the amount of water is directly proportional to the number of cups of rice. This means that the ratio of water to rice cups remains the same throughout the relationship.
Let's calculate the ratio for the given point (1/2, 1):
Ratio of water to rice cups = (Amount of water)/(Number of cups of rice) = 1/(1/2) = 2
Now, let's check the answer choices to find another point with the same ratio:
A: (2, 6) => Ratio of water to rice cups = 6/2 = 3 ❌ (not the same ratio)
B: (3/2, 3) => Ratio of water to rice cups = 3/3/2 = 2 ✅ (same ratio)
C: (1/4, 2) => Ratio of water to rice cups = 2/(1/4) = 8 ❌ (not the same ratio)
D: (2/3, 4) => Ratio of water to rice cups = 4/(2/3) = 6 ❌ (not the same ratio)
So, the point (3/2, 3) is another point on the graph with the given ratio.
Answer: B: (3/2, 3)