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
Options:
(1/4,2)
(3/2,3)
(2,6)
(2/3,4)
To find another point on the graph, we need to set up a proportion using the given coordinate (1/2, 1) and another unknown coordinate (x, y).
According to the proportional relationship, we can set up the following proportion:
(1/2) / 1 = x / y
To find the value of x and y, cross multiply:
1 * x = (1/2) * y
x = y/2
We have x = y/2 as our equation, which means that if y is a multiple of 2, then x will be y divided by 2.
Going through each of the options, we can see which one satisfies the equation:
1. (1/4, 2):
1/4 is not a multiple of 2, so it does not satisfy the equation.
2. (3/2, 3):
3/2 is not a multiple of 2, so it does not satisfy the equation.
3. (2, 6):
6 is a multiple of 2, so it satisfies the equation. x = 6/2 = 3.
4. (2/3, 4):
2/3 is not a multiple of 2, so it does not satisfy the equation.
Therefore, the point (2, 6) is another point on the graph.
To find another point on the graph of this proportional relationship, we can use the given information that the amount of water is directly proportional to the number of cups of rice. This means that for every increase in the number of cups of rice, there will be a corresponding increase in the amount of water.
We are given the coordinate (1/2, 1) on the graph. This means that when there is 1/2 cup of rice, there is 1 cup of water. To find another point, we need to find a related coordinate where the ratio of water to rice cups is the same.
Let's check the options:
- Option (1/4, 2): In this case, the ratio of water to rice cups is 2 cups of water for 1/4 cup of rice, which is different from the ratio in the given coordinate (1/2, 1).
- Option (3/2, 3): Here, the ratio of water to rice cups is 3 cups of water for 3/2 cups of rice, which is also different from the ratio in the given coordinate.
- Option (2, 6): This option has a ratio of 6 cups of water for 2 cups of rice, which is the same as the original coordinate's ratio of 1 cup of water for 1/2 cup of rice. Therefore, this is not the correct answer.
- Option (2/3, 4): This option has a ratio of 4 cups of water for 2/3 cups of rice, which again is different from the original coordinate's ratio.
Therefore, none of the options provided have the same ratio of water to rice cups as the original coordinate.
To identify another point on the graph, we need to find a point that satisfies the proportional relationship between the amount of water and the number of cups of rice.
Given that the amount of water is directly proportional to the number of cups of rice, we can use the formula:
Amount of water = k * Number of cups of rice
Where "k" is the constant of proportionality.
Using the coordinate (1/2, 1) on the graph, we can substitute the values into the formula to solve for "k":
1 = k * 1/2
Multiplying both sides by 2:
2 = k
Now that we know the value of "k" is 2, we can use it to find another point on the graph. Let's check each of the options:
For (1/4, 2):
Amount of water = k * Number of cups of rice
= 2 * 1/4
= 1/2
This does not match the given coordinate, so (1/4, 2) is not another point on the graph.
For (3/2, 3):
Amount of water = k * Number of cups of rice
= 2 * 3/2
= 3
This matches the given coordinate, so (3/2, 3) is another point on the graph.
For (2, 6):
Amount of water = k * Number of cups of rice
= 2 * 2
= 4
This does not match the given coordinate, so (2, 6) is not another point on the graph.
For (2/3, 4):
Amount of water = k * Number of cups of rice
= 2 * 2/3
= 4/3
This does not match the given coordinate, so (2/3, 4) is not another point on the graph.
Therefore, the correct answer is (3/2, 3).