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 ldentify another point on the graph. (2,6) (1/4,2) (2/3,4) (3/2,3)
The point (2,6) is another point on the graph of this proportional relationship.
To find another point on the graph of this proportional relationship, we can use the given statement that the amount of water is directly proportional to the number of cups of rice. This means that the ratio of water to cups of rice remains constant.
Let's use the given point (1/2,1) to determine the constant of proportionality:
Ratio of water to cups of rice = Amount of water / Number of cups of rice
We have (1/2,1) as a coordinate on the graph, which means when the number of cups of rice is 1, the amount of water is 1/2.
Using this information, we can write the proportionality equation as:
Amount of water = k × Number of cups of rice
Substituting the values, we get:
1/2 = k × 1
Simplifying, we find that k = 1/2.
Now, let's use this value of k to find another point on the graph. We can substitute k into the equation to get:
Amount of water = (1/2) × Number of cups of rice
Let's test the given options:
A. (2,6)
Amount of water = (1/2) × 2 = 1
This does not match the given point (2,6).
B. (1/4,2)
Amount of water = (1/2) × (1/4) = 1/8
This does not match the given point (1/4,2).
C. (2/3,4)
Amount of water = (1/2) × (2/3) = 1/3
This does not match the given point (2/3,4).
D. (3/2,3)
Amount of water = (1/2) × (3/2) = 3/4
This does match the given point (3/2,3).
Therefore, the correct answer is (3/2,3).
To identify another point on the graph, we can use the given information about the proportional relationship between the amount of water and the number of cups of rice.
In a proportional relationship, if (a,b) is one point on the graph, then any other point (x,y) on the graph can be found using the formula: y = kx, where k is the constant of proportionality.
In this case, we are given the point (1/2,1) on the graph. So, we can use this information to find the constant of proportionality (k) in the equation y = kx.
To find k, we can substitute the coordinates of the given point (1/2,1) into the equation:
1 = k * (1/2)
Simplifying this equation, we get:
1 = k/2
k = 2
Now we know the constant of proportionality (k) is 2. Therefore, the equation representing the proportional relationship is:
y = 2x
To find another point on the graph, we can choose any value of x and calculate the corresponding y using this equation.
Let's take the first option: (2,6).
Using the equation y = 2x, we substitute x = 2:
y = 2 * 2
y = 4
Therefore, the point (2,6) is on the graph of the proportional relationship.
In summary, the ordered pair (2,6) is another point on the graph of the given proportional relationship.