In the context of Cartesian coordinates, the x-axis represents the horizontal distance or the abscissa. This axis is perpendicular to the y-axis, which denotes the vertical distance or the ordinate. The value of x in a coordinate pair (x, y) indicates the distance of a point from the y-axis along the horizontal plane. For instance, in the coordinate pair (3, 4), the x-coordinate is 3, signifying that the point is 3 units to the right of the y-axis.

The reason for this representation lies in the historical development of the Cartesian coordinate system, which was introduced by René Descartes in the 17th century. Descartes sought to create a system that could represent geometric figures algebraically, and the x-axis was a fundamental component of this system. The use of the x-axis to denote horizontal distance is consistent with the convention of using the first letter of a variable to represent the independent variable, which in this case is the horizontal position.

Data from various educational resources and historical texts confirm the significance of the x-axis in representing horizontal distance. For example, the book "Calculus: Early Transcendentals" by James Stewart and Daniel Clegg states, "The x-axis is the horizontal axis, and the y-axis is the vertical axis. The coordinates of a point are given as an ordered pair (x, y)." This aligns with the convention that the x-coordinate represents the horizontal distance in a Cartesian coordinate system.