independent variable

The independent variable is the one you get to choose. It is the dial you turn, the input you set freely before the function responds. In y = f(x), the letter x is the independent variable: you pick its value, and everything else follows from your choice.

It is called independent because its value is not determined by anything else in the relationship — it depends on nothing inside the problem; you supply it. The other variable then dances to its tune. By convention the independent variable is usually plotted along the horizontal axis of a graph.

Choosing which quantity is independent is a modelling decision, not a fixed law. If you study how distance depends on time, time is independent. But if you were instead asking what time corresponds to a given distance, you could flip the roles. The mathematics adapts to the question you are asking.