Final answer:
By examining the rate of change between the given Y values, we can see that the changes are not constant, thus ruling out a linear relationship. However, the ratio of the changes between the Y values is constant, indicating that this is an exponential relationship.
Step-by-step explanation:
To determine whether the relationship between the X and Y values given is linear, exponential, or neither, we can look at the rate of change between the points. A linear relationship will have a constant rate of change, while an exponential relationship will have a rate of change that itself grows or decays at a constant ratio.
Looking at the X values (9, 17, 25, 33) and the corresponding Y values (-6, -24, -96, -384), we check the differences between consecutive Y values:
- Between -6 and -24, the change is -18.
- Between -24 and -96, the change is -72.
- Between -96 and -384, the change is -288.
These changes are not constant, so the relationship is not linear. Instead, if we divide each change by the previous one, we can see if there is a consistent ratio:
- -72 / -18 = 4
- -288 / -72 = 4
Since the ratio is constant, this indicates an exponential relationship, with each Y value being 4 times the previous Y value for a constant increase in X.