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Lowercase. Don't hyphenate.
Usually refers to the vertical axis in 2D charts and graphs, which shows the values being measured or compared. Refer to it as the value (y) axis on the first mention. On subsequent mentions, use y-axis. It's OK to use vertical (y) axis in content for a general audience.
Don't use italic formatting for the y in y-axis unless the entire word is italic.
In 3D charts, the z-axis is usually the value axis.
See also category axis, z-axis