Y-axis is dated 1875 in MWCD10.
Y-axis is found in "Law of Facility of Errors in Two Dimensions [Continued]," E. L. de Forest, The Analyst, Vol. 8, No. 3. (May, 1881), pp. 73-82 [JSTOR].
Y-COORDINATE. See x-coordinate.
Y-INTERCEPT. Isaac Todhunter refers to "the intercept on the axis of y" in the 7th ed. of A Treatise on Plane Co-ordinate Geometry (1881).
y-intercept is found in 1924 in Analytic Geometry by Arthur M. Harding and George W. Mullins: "Find the equation of the line ... whose slope is 2/3 and whose y intercept is -3."
The term YOUDEN SQUARE was used by R. A. Fisher and F. Yates in the introduction to their Statistical Tables (1938). The term was coined by Ronald Aylmer Fisher (1890-1962) and was named for William John Youden (1900-1971) (DSB, article: "Youden").