Final answer:
The two ordered pairs that represent a directly proportional relationship are B. (2, 1) and (4, 2), as they have a consistent ratio of 1/2.
Step-by-step explanation:
The question is asking which two ordered pairs represent a directly proportional relationship. A directly proportional relationship is one where the ratio between the y-value and the x-value (y/x) remains constant across ordered pairs. This constant value is known as the proportionality constant, or k.
Let's analyze the given pairs:
- A. (4, 2) and (4, 2) - This represents the same point repeated and does not provide information about a proportional relationship.
- B. (2, 1) and (4, 2) - To check for proportionality, divide the y-value by the x-value for both pairs: 1/2 for the first pair and 2/4 for the second pair. Simplified, both ratios equal 1/2, indicating a proportional relationship with a constant proportionality factor of 1/2.
- C. (3, 1) and (4, 2) - The ratios here are 1/3 and 2/4, which simplify to 1/3 and 1/2, respectively. These are not equal, so these pairs are not proportional.
- D. (2, 1) and (4, 3) - The ratios are 1/2 and 3/4, and since these do not equal, these pairs are also not proportional.
Therefore, the correct answer is B. (2, 1) and (4, 2) as they form a proportional relationship.