Question
The amount of water is directly proportional to the number of cups of rice. The coordinate (12, 1) is on the graph of this proportional relationship. Identify another point on the graph.(1 point)
Responses
(14, 2)
Left Parenthesis Start Fraction 1 over 4 End Fraction comma 2 Right Parenthesis
(23, 4)
Left Parenthesis Start Fraction 2 over 3 End Fraction comma 4 Right Parenthesis
(32, 3)
Left Parenthesis Start Fraction 3 over 2 End Fraction comma 3 Right Parenthesis
(2, 6)
Left Parenthesis 2 comma 6 Right Parenthesis
(14, 2)
To identify another point on the graph, we can use the concept that the amount of water is directly proportional to the number of cups of rice. We can use the given coordinate (12, 1) to find the proportionality constant.
Let's use the formula for direct proportionality, which is y = kx, where y is the amount of water, x is the number of cups of rice, and k is the constant of proportionality.
By substituting the given coordinate (12, 1) in the formula, we can solve for k:
1 = k * 12
k = 1/12
Now that we have the value of k, we can find another point on the graph. Let's choose the coordinate (14, 2) and see if it satisfies the proportional relationship:
2 = (1/12) * 14
2 = 14/12
2 = 7/6
Since 2 is equal to 7/6, the coordinate (14, 2) is not on the graph.
We need to pick another option. Let's try the coordinate (32, 3):
3 = (1/12) * 32
3 = 32/12
3 = 8/3
The coordinate (32, 3) satisfies the proportional relationship. Therefore, the correct answer is option (C) (32, 3).
To find another point on the graph, we can use the fact that the amount of water is directly proportional to the number of cups of rice. This means that the ratio between the amount of water and the number of cups of rice remains constant.
Given the point (12, 1), we can set up a proportion to find another point on the graph. Let's call the amount of water "w" and the number of cups of rice "r":
w/12 = 1/1
To find the corresponding values for another point on the graph, we can use this proportion. Let's try each of the answer choices:
(14, 2):
w/14 = 2/1
Cross-multiplying, we get w = 28/1 = 28. The ratio is not the same as the original point, so this is not a valid point.
(23, 4):
w/23 = 4/1
Cross-multiplying, we get w = 92/1 = 92. The ratio is not the same as the original point, so this is not a valid point.
(32, 3):
w/32 = 3/1
Cross-multiplying, we get w = 96/1 = 96. The ratio is not the same as the original point, so this is not a valid point.
(2, 6):
w/2 = 6/1
Cross-multiplying, we get w = 12/1 = 12. The ratio is the same as the original point, so this is a valid point.
Therefore, the correct answer is (2, 6).