Final answer:
The table does not represent a linear relationship because the rate of change (slope) is not constant between different pairs of points.
Step-by-step explanation:
The question asks if the given table represents a linear relationship, and if so, to state the rate of change. To determine if a relationship is linear, you can calculate the rate of change (slope) between points to see if it stays constant. In a linear relationship, the slope between any two points on the line should be the same. The slope is calculated as the change in y divided by the change in x (rise over run).
For the given table, we can take two points and calculate the slope. For instance, let's take the points (2, -6) and (9, -3). The slope is calculated as follows:
Slope = (Y2 - Y1) / (X2 - X1) = (-3 - (-6)) / (9 - 2) = 3 / 7, which is not constant as it's different when we take another set of points such as (16, 0) and (23, 3), which gives us a slope of 3 / 7.
Since the rate of change is not the same between different pairs of points, the relationship is not linear. Therefore, the correct answer is that the table does not represent a linear relationship.