When dealing with statements containing two variables, it often helps to visualize solution sets by turning pairs of numbers into physical locations. The standard way to do this is by assigning the first number to a horizontal distance and the second number a vertical distance. We measure these distances from a starting point, aptly called the origin, which represents both variables having a value of zero. With two variables and values, it is important to track which value is assigned to which variable, so the order of the written values is important - and since there are two of them we have the term ordered pair. The individual numbers in the pair are called coordinates. It is traditional, but not necessary, to use x and y as our variables, but do not rely on these names as many problems and applications encourage the use of all sorts of variable names. While there exists fancy vocabulary to name the coordinates I will often use the phrases "first coordinate" and "second coordinate".
Similarly, when number lines are used to indicate the framework of the coordinate system, I will say "horizontal axis" and "vertical axis" although calling them the "x and y axes" are common. The horizontal axis is placed with positive numbers to the right and negatives to the left. The vertical axis has positives up and negatives down. The coordiante plane (a flat two-dimesional space) is divided up into four quadrants named I−IV starting with the set of pairs having both coordinates positive and moving counterclockwise around the origin.