Final answer:
Upon calculation, the ratios of y/x for the given pairs of x and y values are not constant. This means that the table does not depict a proportional relationship, and none of the provided equations (A, B, C, D) represent the relationship in the table.
Step-by-step explanation:
To determine which equation represents the proportional relationship displayed in the given table (x: 4, 9, 11, 14; y: 3, 2, 7, 8), we need to establish the constant of proportionality, often called the slope or rate, in the potential linear equation of the form y = mx. A proportional relationship means that the ratios (y/x) across the table will be constant (the same for all pairs of values).
For the first pair (x = 4, y = 3), the ratio is 3/4 = 0.75. Checking the rest:
- 9: 2/9 = 0.222 (which is different, so it's not proportional)
- 11: 7/11 = 0.636 (again different)
- 14: 8/14 = 0.571 (different as well)
Since the ratios are not constant, there is no proportional relationship present in the table, so none of the given options (A, B, C, D) correctly represents a proportional relationship for the given pairs of x and y. The given table depicts a non-proportional relationship so we cannot describe it using any of the provided equations which are all of the form y = mx, suggesting a proportional relationship.