My questions are:
why are variables useful in algebra?
Also, what makes the use of variables difficult to understand?
Variables are things that change or vary.
Depending on which variables concern you, you might want to be able to predict just how they vary, and what factors influence this variation. Often finding these factors is difficult and finding how they fit into a formula is very difficult. This can be anything from calculating the potency of a drug to finding out how much heat is needed to keep a swimming pool at a desired temperature.
I hope this helps. Thanks for asking.
Is every linear relationship a direct variation? Why or why not?