ordered pair
An ordered pair is a two-part address for a point, written (x, y). Like “floor 3, room 2” in a building, the two numbers play different roles, and switching them sends you somewhere else.
The first number, x, is the horizontal position (how far left or right of the origin). The second number, y, is the vertical position (how far up or down). The word “ordered” is the whole point: (a, b) means the same as (b, a) only when a equals b.
Ordered pairs let us turn geometry into bookkeeping. A relation or function is just a collection of ordered pairs, and graphing means placing each one as a dot on the coordinate plane.
(3, 7) and (7, 3) are different points: the first is 3 right and 7 up; the second is 7 right and 3 up.
Swapping the entries gives a different location.
Do not confuse the point (2, 3) with the open interval (2, 3) on a number line. The notation looks identical; context tells you which is meant.