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.(1 point)
Responses
A (1/4, 2)
B (3/2, 3)
C (2, 6)
D (2/3, 4)
To find another point on the graph, we can use the fact that the relationship is directly proportional. This means that the ratio between the amount of water and the number of cups of rice will always be the same.
Let's use the given point (1/2, 1) to find this ratio:
Amount of water / Number of cups of rice = 1/2 / 1 = 1/2
Now, we can use this ratio to find another point on the graph. Let's choose option C and see if it satisfies the ratio:
Amount of water / Number of cups of rice = 2 / 6 = 1/3
Since the ratio of 1/3 is not equal to 1/2, option C (2, 6) is not another point on the graph.
Let's try with option A:
Amount of water / Number of cups of rice = 1/4 / 2 = 1/8
The ratio of 1/8 is also not equal to 1/2, so option A is also not another point on the graph.
Let's try with option B:
Amount of water / Number of cups of rice = 3/2 / 3 = 1/2
The ratio of 1/2 is equal to 1/2, so option B (3/2, 3) is another point on the graph.
Therefore, the correct answer is B (3/2, 3).
To identify another point on the graph, we can find a point that satisfies the proportional relationship between the amount of water and the number of cups of rice.
Given that the coordinate (1/2, 1) is on the graph, we can set up a proportion:
(1/2) / 1 = x / y
Simplifying the proportion:
1/2 = x / y
To find another point, we can choose a value for x and solve for y.
Let's plug in x = 1/4:
1/2 = 1/4 / y
To solve for y, we can cross-multiply:
(1/2) * y = 1/4
y/2 = 1/4
Multiplying both sides by 2:
y = 1/2
Therefore, the point (1/4, 1/2) satisfies the proportional relationship.
The correct answer is A (1/4, 2).
To identify another point on the graph of this proportional relationship, we can use the proportional constant.
Given that the amount of water is directly proportional to the number of cups of rice, we can set up a proportion using the coordinates given:
(1/2, 1) and (x, y)
The proportion can be written as:
1/2 = 1/x
To solve for x, we can cross multiply:
2 * 1 = 1 * x
2 = x
So the x-coordinate of the other point is 2.
Next, we need to find the corresponding y-coordinate. Since the relationship is directly proportional, we can use the given proportion constant to find y.
The proportion constant can be calculated using the previous coordinate pair (1/2, 1) as follows:
proportion constant = y / x = 1 / (1/2) = 2
Now, we can use the proportion constant to find the y-coordinate for the new point:
y = proportion constant * x = 2 * 2 = 4
Therefore, the other point on the graph is (2, 4).
Looking at the given options,
A (1/4, 2): The x-coordinate does not match and is not a valid point on the graph.
B (3/2, 3): The x-coordinate does not match and is not a valid point on the graph.
C (2, 6): The x-coordinate matches, but the y-coordinate does not match and is not a valid point on the graph.
D (2/3, 4): The x-coordinate does not match and is not a valid point on the graph.
Therefore, the correct answer is (2, 4), making option D the correct choice.