The horizontal line is the x-axis and the vertical is the y-axis. Study the diagram carefully as you note each of the following facts. Perpendicular means that two lines are at right angles to each other. This system is composed of two number lines that are perpendicular at their zero points. This scheme is called the Cartesian coordinate system (for Descartes) and is sometimes referred to as the rectangular coordinate system. Rene Descartes (1596-1650) devised a method of relating points on a plane to algebraic numbers. Note that this concept contains elements from two fields of mathematics, the line from geometry and the numbers from algebra. We have already used the number line on which we have represented numbers as points on a line. Given a point on the Cartesian coordinate system, state the ordered pair associated with it.Given an ordered pair, locate that point on the Cartesian coordinate system.Represent the Cartesian coordinate system and identify the origin and axes.Upon completing this section you should be able to: We will now study methods of solving systems of equations consisting of two equations and two variables. Given an equation, plugging in x = 0 and solving for y will yield the y-intercept and plugging in y = 0 and solving for x will yield the x-intercept.In previous chapters we solved equations with one unknown or variable. The y-coordinate of an x-intercept is always 0, and the x-coordinate of a y-intercept is always 0. Likewise, the y-intercept is a point at which a graph intercepts the y-axis. The x-intercept is a point at which a graph intercepts the x-axis. Once we can plot points in the coordinate plane, we can move on to graphing more complicated objects, since a graph of a line or some other function is simply a visual representation of all the points, or ordered pairs, that make up the function. Then, we can plot the point by counting the appropriate number of units along the x- and y-axes. Thus, to plot a point on a coordinate plane, we simply need to know the ordered pair.

For point C, move to the right 4 units on the x-axis to get an x-coordinate of 4, then move down 4 units on the y-axis to get a y-coordinate of -4.Since there is no vertical distance to move on the y-axis the y-coordinate is 0. For point B, move to the left 4 units on the x-axis to get an x-coordinate of -4.For point A, move to the right 3 units on the x-axis to get an x-coordinate of 3, then move up 4 units on the y-axis to get a y-coordinate of 4.

The red arrows indicate how we move from the origin to a given point in the coordinate plane, as described below. Consider points A, B, and C graphed in the coordinate plane below. In other words, (x, y) is not the same as (y, x). Note that the reason it is called an ordered pair is because the x-value must come first, followed by the y-value. In an ordered pair, the x and y-values are enclosed within parenthesis and separated by a comma. Where x is the x-value and y is the y-value. An ordered pair is a pair of values in which the first value indicates the x-coordinate and the second indicates the y-coordinate. Ordered pairsĪ given point in the coordinate plane is designated using what is referred to as an ordered pair. It is therefore important to pay attention to the axis markings, since differences in selected axes intervals can significantly impact the shape of a given graph. The y-axis in this same example could even have tick marks that represent 3 units the x-axis and the y-axis do not have to have the same interval between marks. In this case, the space between each tick mark represents 2 units. For example, instead of the x-axis counting up by 1, the first tick mark to the right of 0 could be labeled 2, the subsequent one 4, and the next 6. It is worth noting that the axes can be labeled in any number of ways, as long as each axis maintains a consistent interval. The above representation of the coordinate plane is one of the most basic forms, where each tick mark on the axis represents 1 unit. They are represented by two number lines that intersect perpendicularly at the origin, located at (0, 0), as shown in the figure below. In two-dimensional space, the x-axis is the horizontal axis, while the y-axis is the vertical axis. Together, they form a coordinate plane, which is the space in which two-dimensional graphing occurs. The x-axis and y-axis are axes in the Cartesian coordinate system. Home / geometry / coordinate plane / x and y axis X and y axis

Graph coordinate plane