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.
O (2, 6)
O (1/4, 2)
O (2/3, 4)
O (3/2, 3)
To find another point on the graph of this proportional relationship, we can use the information given and set up a proportion.
Given that the coordinate (1/2, 1) is on the graph, we know that when there are 1 cup of rice, there is 1/2 cup of water.
If we let x be the number of cups of rice and y be the amount of water, we can set up the proportion:
x/y = 1/2
Now, we can substitute the answer choices into this proportion to see which one yields a true statement.
A) (2, 6): 2/6 = 1/2 --> this is not true.
B) (1/4, 2): 1/4 / 2 = 1/2 --> this is true.
C) (2/3, 4): 2/3 / 4 = 1/2 --> this is not true.
D) (3/2, 3): 3/2 / 3 = 1/2 --> this is not true.
Therefore, the correct answer is (1/4, 2), so the another point on the graph is (1/4, 2).
To identify 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.
We can set up a proportion using the coordinates of the known point (1/2, 1) and solve for the unknown point in the form (x, y).
Given point: (1/2, 1)
Unknown point: (x, y)
Using the proportion, we have:
(1/2) / 1 = y / x
Simplifying the proportion:
1/2 = y / x
To find another point on this line, we can choose any value for x and solve for the corresponding value of y.
Let's choose x = 2:
1/2 = y / 2
y = 1
Therefore, another point on the graph is (2, 1).
Among the answer choices provided, none match the coordinates (2, 1) for another point on the graph.
To find another point on the graph of the proportional relationship between the amount of water and the number of cups of rice, we can use the given information and apply it to the choices provided.
The given information states that the amount of water is directly proportional to the number of cups of rice. This means that the ratio of water to rice remains constant. In other words, if we multiply the number of cups of rice by a certain factor, we must also multiply the amount of water by that same factor.
Let's calculate the constant of proportionality using the given coordinate (1/2, 1):
(1/2 cups of rice) * constant = 1 cup of water
To solve for the constant, we divide both sides of the equation by (1/2):
constant = 1 / (1/2)
constant = 2
Now, let's check each of the answer choices to find another point:
O (2, 6):
(2 cups of rice) * constant = 2 * 2 = 4 cups of water
O (1/4, 2):
(1/4 cup of rice) * constant = (1/4) * 2 = 1/2 cup of water
O (2/3, 4):
(2/3 cups of rice) * constant = (2/3) * 2 = 4/3 cups of water
O (3/2, 3):
(3/2 cups of rice) * constant = (3/2) * 2 = 3 cups of water
From the calculations above, we can see that the point (2, 6) satisfies the proportional relationship. Therefore, the answer is:
O (2, 6)