Final answer:
The ordered pairs that represent a proportional relationship are (2, 1) and (4, 2), which are found in Option C. This is because the ratio of 2 to 1 is equal to the ratio of 4 to 2, indicating a constant rate of change and therefore a proportional relationship.
Step-by-step explanation:
Two ordered pairs represent a proportional relationship if the ratio of the first numbers (the x-values) to the second numbers (the y-values) is the same in both pairs. This means that for two pairs (a, b) and (c, d), the relationship is proportional if and only if a: b = c : d, which means a / b = c / d. Among the given options, we can check for proportionality by computing the ratios: Option A: (4, 2) and (4, 2) have the same elements, so technically the ratio is 1, but since the x-values are not changing, this does not represent a varying proportional relationship. Option B: (3, 1) and (4, 2), the ratio of x to y for both pairs is 3/1 and 4/2, which simplifies to 3 and 2, not the same, hence not proportional. Option C: (2, 1) and (4, 2), where the ratio is 2/1 and 4/2, which simplifies to 2 and 2. Since the ratios are equal, this represents a proportional relationship. Option D: (2, 1) and (4, 3), the ratio is 2/1 and 4/3 and these are not equal, hence not proportional. Therefore, the ordered pairs that represent a proportional relationship are found in Option C: (2, 1) and (4, 2).