Need help with this problem. How to find out what equation they are.

a linear equation will have only one possible value for x given y. for example D is linear. (3xy=4) if you chose 1 as your value for y then x MUST be 4/3. so when the highest power of x is one (X^1), then the equation is linear. equation C is also linear

a quadratic equation will have two possible answers. B is quadratic because if you replace f(x) with a value such as -2, you will have two possible answers for x, 2 OR -2. the highest power of x in this equation is 2 (X^2), therefore it is quadratic

any equation having powers of x higher than two will not be quadratic, or any equation having powers lower than zero. for example equation A would be "other" because the power of x is -1. this is due to the x value being in the denominator. therefor x^-1 makes that equation neither linear or quadratic 

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.