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In a cartesian coordinate system, the $x$-axis is the one usually depicted and visualised as going from left to right.

It consists of all the points in the real vector space in question (usually either $\R^2$ or $\R^3$) at which all the elements of its coordinates but $x$ are zero.

Also see

Linguistic Note

The plural of axis is axes, which is pronounced ax-eez not ax-iz.

Compare basis.