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
(32, 3)
Left Parenthesis Start Fraction 3 over 2 End Fraction comma 3 Right Parenthesis
(2, 6)
Left Parenthesis 2 comma 6 Right Parenthesis
(23, 4)
(14, 2)
To find another point on the graph of this proportional relationship, we can use the given coordinate (12, 1) and the fact that the amount of water is directly proportional to the number of cups of rice. We can set up a proportion using this information.
Let's assume that x represents the number of cups of rice and y represents the amount of water. Using the given coordinate (12, 1), we have the proportion:
12 cups of rice / 1 cup of water = x cups of rice / y cups of water
To find another point on the graph, we can choose a value for cups of rice (x) and solve for cups of water (y) using the proportion.
Let's choose 14 cups of rice (x = 14):
12/1 = 14/y
Cross multiply: 12 * y = 1 * 14
12y = 14
Divide both sides by 12: y = 14/12 = 7/6
So another point on the graph is (14, 7/6) or approximately (14, 1.17).
Therefore, the correct answer is (14, 2).
To find another point on the graph of this proportional relationship, we can use the concept of direct proportionality.
In a direct proportion, the ratio of the two variables remains constant. In this case, the amount of water is directly proportional to the number of cups of rice. So, if we increase the number of cups of rice by a certain factor, the amount of water should also increase by the same factor.
Given that the coordinate (12, 1) is on the graph, it means that when there are 12 cups of rice, there is 1 unit of water. We can use this information to find another point.
Let's take the option (14, 2). This means that when there are 14 cups of rice, there are 2 units of water. The ratio of water to rice cups is 1:12 for the first point, and 2:14 for the second point. Simplifying both ratios, we can see that they are equal: 1/12 = 2/14.
This confirms that (14, 2) is indeed another point on the graph of the proportional relationship. So, the correct answer is (14, 2).