Which statement best defines direct variation?

A situation in which $y$ and $x$ are unrelated but accidentally show similar numerical trends over a small sample.

A quadratic relationship where $y$ depends on the square of $x$ and the constant $k$ changes with $x$.

A relationship where $y$ equals $k$ divided by $x$ for all nonzero $x$, meaning one variable increases while the other decreases and they never change in the same direction under any circumstance.

A linear relationship of the form $y=kx$ where $k$ is a fixed constant and $y$ and $x$ increase or decrease together.