Is y equals 2 to the x power a linear equation?

If you mean y = 2^x, then no, it is not a linear equation. This is an exponential equation. The graph of this exponential equation would start out near zero on the left-hand side (there is a horizontal asymptote at y = 0) and would gradually increase as you move to the right: overall, it has a curved shaped.

If you mean y = 2x, then yes, it is a linear equation.