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)
To find another point on the graph, we can use the proportionality between the amount of water and the number of cups of rice.
Since the amount of water is directly proportional to the number of cups of rice, we can write the proportionality as:
water/cups of rice = k
where k is the constant of proportionality.
We are given that the coordinate (1/2, 1) is on the graph, which means that at (1/2) cup of rice, there is 1 unit of water. Therefore, we can write the following equation using the proportionality:
1/2 / 1 = k
Simplifying the equation, we find that:
1/2 = k
So, the constant of proportionality is k = 1/2.
To find another point on the graph, we can choose any value for the number of cups of rice and use the proportionality to find the corresponding amount of water.
For example, if we let the number of cups of rice be 2, we can find the corresponding amount of water using the proportionality:
water/cups of rice = k
water/2 = 1/2 (since k = 1/2)
Multiplying both sides of the equation by 2, we get:
water = 1
Therefore, at 2 cups of rice, there is 1 unit of water.
So, another point on the graph is (2, 1).
To find another point on the graph, we can use the fact that the relationship is directly proportional, which means that the ratio between the amount of water and the number of cups of rice is constant.
Given that the coordinate (1/2, 1) is on the graph, it represents a specific relationship between the amount of water and the number of cups of rice. In this case, it means that when there are 1/2 cups of water, there is 1 cup of rice.
To find another point on the graph, we can use this ratio to find another value for the amount of water when the number of cups of rice is different. Let's say we want to find the point on the graph when there are 2 cups of rice.
Since the ratio is constant, we can set up a proportion:
(amount of water) / (number of cups of rice) = (amount of water at coordinate (1/2, 1)) / (number of cups of rice at coordinate (1/2, 1))
Let's substitute the values from the given coordinate:
(amount of water) / 2 = (1/2) / 1
Simplifying the equation:
(amount of water) / 2 = 1/2
Cross-multiplying:
(amount of water) = 2/2
(amount of water) = 1
Therefore, when there are 2 cups of rice, there will be 1 cup of water. This gives us another point on the graph, which is (1, 2).
To identify another point on the graph, we need to understand what it means for two quantities to be directly proportional. In this case, we know that the amount of water is directly proportional to the number of cups of rice.
The fact that this relationship is directly proportional means that as the number of cups of rice increases or decreases, the amount of water will also increase or decrease by the same factor. In other words, the ratio of water to rice cups will remain constant.
Let's use the given coordinate (1/2, 1) to find the constant of proportionality. The coordinate represents that when there is half a cup of rice (1/2), there is one cup of water (1).
To find the constant of proportionality, we can divide the amount of water by the number of cups of rice. In this case, 1 divided by (1/2) is equal to 2.
Now, we can use this constant of proportionality to find another point on the graph. Let's choose a different value for the number of cups of rice and calculate the corresponding amount of water.
For example, if we choose 2 cups of rice, we can multiply it by the constant of proportionality:
2 cups of rice * 2 (constant of proportionality) = 4 cups of water
Therefore, the coordinate (2, 4) represents another point on the graph of this proportional relationship.
So, another point on the graph is (2, 4).