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.
(1/4, 2)
(3/2, 3)
(2/3, 4)
(2, 6)
To determine another point on the graph, we need to find a point that satisfies the direct proportionality relationship between the amount of water and the number of cups of rice.
We can do this by using the given information of the coordinate (1/2, 1), which means that when there is 1/2 unit of water, there is 1 cup of rice. We can then find the constant of proportionality by dividing the number of cups of rice by the amount of water. In this case, the constant of proportionality is 1/2.
We can use this constant to find the amount of water for the other options:
Option 1: (1/4, 2)
2 cups of rice / 1/4 unit of water = 8 cups of rice per unit of water. Since the constant of proportionality is 1/2, this point does not satisfy the direct proportionality.
Option 2: (3/2, 3)
3 cups of rice / 3/2 units of water = 2 cups of rice per unit of water. Since the constant of proportionality is 1/2, this point satisfies the direct proportionality.
Option 3: (2/3, 4)
4 cups of rice / 2/3 units of water = 6 cups of rice per unit of water. Since the constant of proportionality is 1/2, this point does not satisfy the direct proportionality.
Option 4: (2, 6)
6 cups of rice / 2 units of water = 3 cups of rice per unit of water. Since the constant of proportionality is 1/2, this point satisfies the direct proportionality.
Therefore, the other point that satisfies the direct proportionality relationship is (3/2, 3).
To identify another point on the graph of the proportional relationship between the amount of water and the number of cups of rice, we need to use the given information that the relationship is directly proportional.
If the relationship is directly proportional, it means that the ratio between the two quantities remains constant. In this case, the ratio between the amount of water and the number of cups of rice should stay the same for any point on the graph.
To find the constant ratio, we can use the given coordinate (1/2, 1). According to the given information, at 1/2 cup of water, there is 1 cup of rice. Therefore, the ratio between the amount of water and the number of cups of rice is 1:1/2, or simply 2:1.
Using this ratio, we can find another point on the graph by finding a value that is in the same proportion. Let's go through each option:
1) (1/4, 2): This option has a ratio of 2:1/4, and simplifying it gives us a ratio of 8:1. However, this does not match the constant ratio we found, so this is not a valid point on the graph.
2) (3/2, 3): This option has a ratio of 3:3/2, which simplifies to 2:1. This matches the constant ratio of 2:1, so this is a valid point on the graph.
3) (2/3, 4): This option has a ratio of 4:2/3, which simplifies to 6:1. This does not match the constant ratio, so this is not a valid point on the graph.
4) (2, 6): This option has a ratio of 6:2, which simplifies to 3:1. This does not match the constant ratio, so this is not a valid point on the graph.
Therefore, the only point on the graph that matches the constant ratio is (3/2, 3).
To find another point on the graph, we need to find a pair of values that satisfy the proportional relationship between the amount of water and the number of cups of rice.
Since the relationship is directly proportional, we can use the given coordinate (1/2, 1) to set up a proportion:
1/2 / 1 = x / y
where x and y represent the other pair of values.
Simplifying this proportion:
1/2 = x / y
To find x when y is 1, we can multiply both sides of the equation by y:
1/2 * y = x
So, if we substitute y = 1:
1/2 * 1 = 1/2 = x
Therefore, another point on the graph is (1/2, 1/2).
None of the given options match this point, so none of them are correct.