The earliest known use of "m" for slope is from an 1844 British text by Matthew O'Brien entitled "A Treatise on Plane Co-Ordinate Geometry". Later in 1848 George Salmon (1819-1904) referred to O'Brien's 1844 article within his "A Treatise on Conic Sections" and used the slope-intercept formula "y = mx + b", where "b" is the ordinate (vertical component) of the point where the line intersects the y-axis. It is also known that the four authors Isaac Todhunter in 1855 (Treatise on Plane Co-Ordinate Geometry), George A. Osborne in 1891 (Differential and Integral Calculus), and Arthur M. Harding and George W. Mullins in 1924 (Analytic Geometry) each used "m" to refer to slope in their mathematical writings.

(Source: http://www.bookrags.com/sciences/mathematics/slope-wom.html)

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