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)

Question

Responses

(2, 6)
Left Parenthesis 2 comma 6 Right Parenthesis

(32, 3)
Left Parenthesis Start Fraction 3 over 2 End Fraction comma 3 Right Parenthesis

(14, 2)
Left Parenthesis Start Fraction 1 over 4 End Fraction comma 2 Right Parenthesis

(23, 4)

Answer 1

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

\[ y = kx \]

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

From the point (12, 1), we can find \( k \):

\[ 1 = k \cdot 12 \]

To find \( k \):

\[ k = \frac{1}{12} \]

Now, we can use this value of \( k \) to determine y for other values of x. If we test the possible points:

1. For (2, 6): \[ y = \frac{1}{12} \cdot 2 = \frac{2}{12} = \frac{1}{6} \] (not correct)

2. For (32, 3): \[ y = \frac{1}{12} \cdot 32 = \frac{32}{12} = \frac{8}{3} \] (not correct)

3. For (14, 2): \[ y = \frac{1}{12} \cdot 14 = \frac{14}{12} = \frac{7}{6} \] (not correct)

4. For (23, 4): \[ y = \frac{1}{12} \cdot 23 = \frac{23}{12} \] (not equal to 4, not correct)

None of these points seem to satisfy the equation of the direct proportionality based on the known point (12, 1).

However, if you multiply both x and y values from the known point (12, 1) by a common factor \( c \) to find another point, \( (12c, c) \), this gives:

Let's check the point (6, 0.5): \[ 0.5 = \frac{1}{12} \cdot 6 = \frac{6}{12} \]

This point is valid (6, 0.5), but not in the options.

It seems either the options given might have an error in the relationship or the problem. Please validate the options or provide new points to resolve this.