The amount of water is directly proportional to the umber of cups of rice. The coordinate (1/2, 1) is on the graph of this proportional relationship. Identify another point of the graph.

Question

A. (1/4, 2)
B. (2/3, 4)
C. (3/2, 3)
D. (2, 6)

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 given point $(1/2,1)$, we can determine $k$:

$$1=k\cdot \frac{1}{2}$$

Solving for $k$:

$$k=1÷\frac{1}{2}=2$$

Thus, the relationship can be described by the equation:

$$y=2x$$

Now we can use this equation to check each of the answer choices:

A. For $(1/4,2)$: $$y=2\cdot \frac{1}{4}=\frac{2}{4}=\frac{1}{2}\text{(not a valid point)}$$

B. For $(2/3,4)$: $$y=2\cdot \frac{2}{3}=\frac{4}{3}\text{(not a valid point)}$$

C. For $(3/2,3)$: $$y=2\cdot \frac{3}{2}=3\text{(this is a valid point)}$$

D. For $(2,6)$: $$y=2\cdot 2=4\text{(not a valid point)}$$

Hence, the only valid point on the graph of this proportional relationship is:

C. (3/2, 3).