Final Answer:
The given dataset does not display a linear relationship between the values of X and Y.
C) The relationship is not linear.
Step-by-step explanation:
Determining linearity in a dataset involves assessing whether the relationship between the variables can be adequately represented by a linear equation (y = mx + b), where 'm' represents the slope and 'b' the y-intercept.
Given the dataset XY: -7, 5, -5, 9, -3, 18, 17, 2, it's crucial to assess if a consistent change in one variable corresponds to a consistent change in the other. To evaluate linearity, a typical method involves plotting the data points on a graph and observing if they form a straight line.
In this case, without a visual plot, we assess the options provided. The options present potential linear equations to model the data relationship. Each equation is in a different form but purportedly represents a linear relationship between X and Y.
Upon inspecting the equations provided in options A, B, C, and D, none conform to the standard linear equation form (y = mx + b) with a consistent slope 'm' and y-intercept 'b'.
For instance, option A offers an equation y - 5 = -2.5(x + 7), but this equation doesn't align with the conventional linear equation format, lacking a clear 'm' value for the slope. Option B, y + 7 = (x - 5), also deviates from the linear equation structure.
Options C indicates the relationship isn't linear, suggesting that the dataset's behavior doesn't fit a straight-line pattern. Given the lack of a suitable linear equation among the choices provided, option C seems more aligned with the observation that the relationship portrayed by the given data isn't linear.
In conclusion, without a clear linear equation fitting the data pattern and none of the provided options conforming to the standard linear equation format, the approach relies on the absence of a consistent linear representation, leading to the conclusion that the relationship exhibited by the given data isn't linear.