Question

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

Answer 1

Since the amount of water is directly proportional to the number of cups of rice, we can express this relationship as:

\[ W = k \cdot R \]

where \( W \) is the amount of water, \( R \) is the number of cups of rice, and \( k \) is the constant of proportionality.

From the point \( (1/2, 1) \), we have:

- \( R = 1/2 \) (cups of rice)
- \( W = 1 \) (amount of water)

Substituting these values into the equation gives us:

\[ 1 = k \cdot \frac{1}{2} \]

To find \( k \), we can multiply both sides by 2:

\[ k = 2 \]

Now we can write the equation of the relationship as:

\[ W = 2R \]

To identify another point on the graph, we can choose a different value for \( R \) and calculate \( W \). For example, let's choose \( R = 1 \):

\[ W = 2 \cdot 1 = 2 \]

Thus, another point on the graph is \( (1, 2) \).

You can choose other values for \( R \) to find even more points. For example:

- If \( R = 2 \): \( W = 2 \cdot 2 = 4 \), giving the point \( (2, 4) \).
- If \( R = 3 \): \( W = 2 \cdot 3 = 6 \), giving the point \( (3, 6) \).

So, any point like \( (1, 2) \), \( (2, 4) \), or \( (3, 6) \) would be valid points on the graph of this proportional relationship.