Final answer:
The function y = 4x^(3/2) is not linear, and its slope varies with x, hence we cannot classify it as parallel or perpendicular without more context. Lines Y2 and Y3 have the same slope and are parallel to each other and to the line of best fit.
Step-by-step explanation:
When discussing the orientation of mathematical functions, we often refer to lines being either parallel or perpendicular. To determine if the function y = 4x(3/2) is parallel or perpendicular, we need to compare its slope with the slopes of other lines in question. In the supplied information, only linear equations would directly have slopes that can be compared. However, the given function is not linear; it is a power function, where the exponent is fractional. The function y = 4x(3/2) does not have a constant slope, as the slope varies depending on the value of x.
Moreover, when it comes to the slope of the lines Y2 and Y3, which are Y2 = -173.5 + 4.83x - 2(16.4) and Y3 = -173.5 + 4.83x + 2(16.4), both lines have the same slope of 4.83. Since they share the same slope as the line of best fit, y = -173.5 + 4.83x, the lines Y2 and Y3 are parallel to each other and to the line of best fit.
Therefore, unless the function y = 4x(3/2) is graphed or compared with another line to understand its directional changes in relation to another line, we cannot definitively say if it is parallel or perpendicular.