Z
I suppose under Cartesian coordinates you want the third dimensional axis I'd refer to as the up/down directions with the x & y axis on the plane of the page...
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The x axis is horizontal and the y axis is vertical.
False.
in or out
For an example, if negative and positive directions on the X and Y axes represent left/right and forward/backward, Z axis represents up/down.
A z-intercept is a point at which a line crosses the z-axis of a Cartesian grid.