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
To find another point on the graph, we can use the given proportionality constant (direct variation constant).
Let's assume the proportionality constant is "k".
Using the given point (1/2, 1), we can set up a proportion:
water / rice = k
1 / (1/2) = k
2 = k
So, the equation for this proportionality relationship is:
water = 2 * rice
To find another point, we can choose a value for rice and find the corresponding value for water.
Let's say we choose rice = 3 cups:
water = 2 * 3 = 6 cups
So, another point on the graph is (3, 6).
write in fraction form
In fraction form, the other point on the graph is (3, 6), which can be written as (3/1, 6/1).
simplify
The simplified fraction form of (3/1, 6/1) is (3, 6)
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
Responses
(2, 6)
(2/3, 4)
(3/2, 3)
(1/4, 2)
To identify another point on the graph, we can use the given coordinate (1/2, 1) and the fact that the relationship is direct proportionality.
Since the amount of water is directly proportional to the number of cups of rice, we can multiply the rice value in the given coordinate by a constant to find another point on the graph. Let's call this constant "k".
For the given coordinate (1/2, 1):
water = k * rice
1 = k * (1/2)
1 = k/2
k = 2
Now we can use this value of k to find another point. Let's choose a value for rice and calculate the corresponding water value:
If we choose rice = 2, then:
water = 2 * 2 = 4
So another point on the graph is (2, 4).
Thus, the answer is (2, 4).
use the responses
To identify another point on the graph using the given responses, we can examine each option and see if it matches the given proportionality.
Option 1: (2, 6)
If the amount of water is directly proportional to the number of cups of rice, then a rice value of 2 should correspond to a water value of 6. However, in the given coordinate (1/2, 1), the water value is 1, not 6. So, option 1 is not the correct point on the graph.
Option 2: (2/3, 4)
If the amount of water is directly proportional to the number of cups of rice, then a rice value of 2/3 should correspond to a water value of 4. However, in the given coordinate (1/2, 1), the water value is 1, not 4. So, option 2 is not the correct point on the graph.
Option 3: (3/2, 3)
If the amount of water is directly proportional to the number of cups of rice, then a rice value of 3/2 should correspond to a water value of 3. However, in the given coordinate (1/2, 1), the water value is 1, not 3. So, option 3 is not the correct point on the graph.
Option 4: (1/4, 2)
If the amount of water is directly proportional to the number of cups of rice, then a rice value of 1/4 should correspond to a water value of 2. This matches the given coordinate (1/2, 1) where the rice value is half of 1/2 (equal to 1/4) and the water value is 1. Therefore, option 4 is the correct point on the graph.
The correct answer is (1/4, 2).