Question

The amount of water is directly proportional to the number of cups of rice. The coordinate 1/2 and one is on the graph of the proportional relationship identify another point on the graph would it be two, 63 over two, three 2/3, four or 1/4, two.

Answer 1

[AI-generated answer — Explain Bot]

To find another point on the graph of the proportional relationship, we can use the concept of direct proportionality. In a direct proportion, the ratio of two variables remains constant. In this case, the amount of water and the number of cups of rice are directly proportional.

Given the coordinates (1/2, 1), which represents one-half cup of water and one cup of rice, we need to find another point that satisfies the same direct proportionality.

To do this, we can set up an equation using the given information and find the constant ratio. Let's assume the constant ratio is represented by the variable "k" (k is a constant).

From the given information, we have:
(1/2) / 1 = k

Simplifying the equation, we have:
k = (1/2) * 1
k = 1/2

Now, we can use this constant ratio of k to find another point. Let's substitute k into the equation:

(1/2, 1) * (k) = (?, ?)

(1/2) / 1 = (1/2) / 1
1 = 1

So, the point (1/2, 1) satisfies the direct proportionality relationship.

Answer 2

[AI-generated answer — Bot GPT 3.5]

To find another point on the graph of the proportional relationship, we can use the given coordinate (1/2, 1) and vary the value of cups of rice while keeping the proportion constant.

Let's assume that the proportionality constant is k.

We can set up a proportion based on the given information:
1/2 * k = 1

Since 1/2 is the number of cups of rice and 1 is the corresponding amount of water, we need to find another pair of values that satisfies this proportion.

To find another point, we can choose a different value for the cups of rice and solve for the corresponding amount of water.

Let's try the options one by one:

1) (two, 63 over two):
two * k = 63 over two
2k = 63/2

This equation does not satisfy the proportion (1/2 * k = 1), so (two, 63 over two) is not another point on the graph.

2) (three 2/3, four):
(3 2/3) * k = 4

To solve for k, we need to convert 3 2/3 to an improper fraction:
3 2/3 = (3 * 3 + 2) / 3 = 11/3
(11/3) * k = 4

Solving this equation, we find:
k = 4 * 3/11 = 12/11

So the corresponding point on the graph would be (three 2/3, four) or (11/3, 4).

Therefore, the answer is three 2/3, four.

3) (1/4, two):
(1/4) * k = 2
k = 2 * 4 = 8

So the corresponding point on the graph would be (1/4, two).

Therefore, the answer is 1/4, two.

In summary, another point on the graph that satisfies the proportional relationship is (three 2/3, four) or (11/3, 4).