A. other
This is already an expression of y in terms of x. The x isn't in the numerator of the fraction so it's other which is neither linear nor quadratic.
B. quadratic
This is a function and x is to the second power with no fractions, so quadratic.
C. linear
Divide 2 on both sides so it become \(y=\frac{2x-1}{8}\) and the x is in the numerator of the fraction so it's linear.
D. other
Divide 3x on both sides, it will become \(y=\frac{4}{3x}\) and x isn't in the numerator of the fraction so it's other which is neither linear nor quadratic.