Does the horizontal axis on a gragh also known as the x-axis?

Yes... More or less. The axes can be called anything; traditionally, the horizontal axis is often called "x", the vertical axis is often called "y", and the vertical component is assumed to be the dependent part ("y" is a function of "x"). However, other combinations are also possible; for example, if there is time involved in the graph, the horizontal axis will usually be the time.