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
a .3/2 , 3
b. 1/4 , 2
c. 2 , 6
d. 2/3 , 4
To find another point on the graph, we need to find a ratio of water to rice that is equivalent to the ratio of 1/2 to 1.
Since the relationship is directly proportional, we can set up a proportion:
water/rice = (1/2)/(1)
Simplifying this proportion, we get:
water/rice = 1/2
Now we can select another point that has a water to rice ratio of 1/2.
Looking at the given options, the point (2, 6) satisfies this condition because 2/6 = 1/2.
Therefore, the answer is c. 2, 6.
To identify 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 the concept of direct proportionality.
In a direct proportion, when one quantity increases or decreases, the other quantity also increases or decreases by the same ratio.
Given that the coordinate (1/2, 1) is on the graph, it means that when there is 1/2 (0.5) cup of rice, there is 1 cup of water. Now, let's find another point on the graph using this proportion.
Take option a: (3/2, 3)
This means that when there are 3/2 (1.5) cups of rice, there are 3 cups of water. To check if this point satisfies the proportionality, we can compare the ratios:
0.5 cup of rice / 1 cup of water = 1.5 cups of rice / 3 cups of water
Since both ratios are equal to 0.5, we can conclude that option a, (3/2, 3), represents another point on the graph of the proportional relationship.
Therefore, the correct answer is a. 3/2, 3.
To identify another point on the graph, we can use the concept of proportionality. Since the amount of water is directly proportional to the number of cups of rice, we can find the proportionality constant (k) by dividing the y-coordinate by the x-coordinate of the given point (1/2, 1):
k = y / x = 1 / (1/2) = 2
Now, we can use this constant to find another point on the graph. Let's check each option by substituting the x-coordinate and multiplying it by the constant (k) to see if it equals the y-coordinate:
a. (3/2, 3): 2 * (3/2) = 3, so (3/2, 3) is a valid point.
b. (1/4, 2): 2 * (1/4) = 1/2, not equal to 2, so (1/4, 2) is not a valid point.
c. (2, 6): 2 * 2 = 4, not equal to 6, so (2, 6) is not a valid point.
d. (2/3, 4): 2 * (2/3) = 4/3, not equal to 4, so (2/3, 4) is not a valid point.
Therefore, the correct answer is option a. Another point on the graph is (3/2, 3).