Answer:
Step-by-step explanation: The relationship between the side lengths of a rectangle, represented by x and y, is linear because the ratio of the side lengths remains constant. In this case, as x doubles from 2 to 4, y also doubles from 4 to 8. Similarly, as x increases by 2 units from 4 to 6, y also increases by 2 units from 8 to 10. This consistent change in both x and y indicates a linear relationship.
b. The relationship between x and the area of the rectangle is neither linear nor exponential because the change in the area does not follow a consistent pattern as x increases. For example, when x increases from 2 to 4, the area increases from 8 to 32, which is a multiplication factor of 4. However, when x increases from 4 to 6, the area increases from 32 to 72, which is a multiplication factor of 2.25. This inconsistency in the change of the area suggests that it does not follow a linear or exponential relationship.
Furthermore, if we observe the data, the multiplication factor for the area does not remain constant as x increases. For instance, when x increases from 2 to 4, the area increases by a factor of 4 (32 divided by 8), but when x increases from 4 to 6, the area increases by a factor of 2.25 (72 divided by 32). This irregular pattern indicates that the relationship between x and the area is not linear or exponential.