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Axis (Graph)Definition & Meaning
Definition
Mathematics defines an axis as a line on which measurements can be made or marked. There are two lines in the coordinate plane that are important: the xaxis and the yaxis. Vertical numbers are represented by the yaxis and horizontal numbers are represented by the xaxis. The coordinate plane is formed by the intersection of these two axes perpendicularly. In coordinate pair (X,Y), X and Y are also referred to as abscissa and ordinate, respectively.
Representation of X and Y Axis
The two basic axes can be represented by the following figure shown below. The horizontal line is making the xaxis (horizontal axis) which is shown by the red line while the vertical line is making the yaxis which is shown by the blue line (vertical axis). Whenever an ordered pair of points is written, the xaxis is written first. Each point on the graph has an ordered pair of xcoordinates leading to ycoordinates with the xaxis corresponding to a point on the graph.
Structure of Coordinates on Axis
In coordinate grids, points are located by using numbers. There are two numbers that identify each point; one number on the xaxis and one number on the yaxis, called the xcoordinate and ycoordinate, respectively. It is common to read coordinates in pairs (x, y) in parentheses. In order to understand the coordinate concept we need to first define the following terms.

Origin
The intersection of the xaxis and yaxis is basically the origin which is usually highlighted by “O”.

Abscissa
Consider a point, Abscissa or x coordinate is its distance from the yaxis with respect to the xaxis.

Ordinate
Consider a point, Ordinate or y coordinate is its distance from the xaxis with respect to the yaxis.
All of the above concepts are illustrated in the figure shown below. Point A where x=0 and y=0 or where the x and y axis intersects is referred to as Origin.While X and Y as abscissa and ordinate respectively.
The Direction of Movements on Axes

Positive XAxis
For the positive xaxis, we will move horizontally toward the right side.

Negative XAxis
For the negative xaxis, we will move horizontally toward the left side.

Positive YAxis
For the positive Yaxis, we will move vertically upward

Negative YAxis
For Negative Yaxis, we will move vertically downward.
Test Point Plotting on Axis
Consider a point P(1,2), below is the illustration of this point on axes. The x coordinate or abscissa is “1” and the y coordinate or ordinate is “2”.So what we will do is that starting from the origin as a reference we will move 1 step right on the horizontal axis (xaxis) and we will move 2 steps upward on the vertical axis (yaxis).
Quadrants
X and Y axis divide the coordinate plane into four different halves which are referred to as quadrants. So there are four quadrants depending upon the positive and negative values of x and y. Below is the Illustration of Quadrants. The above figure shows the illustration of quadrants

Quadrant 1
The top right portion of the graph is known as the first quadrant. In this region the value of numbers lying on x and y on both axes are positive.

Quadrant 2
The top left portion of the graph is known as the second quadrant. In this region, the value of numbers lying on the xaxis is negative while the value of numbers lying on the yaxis is positive.

Quadrant 3
The bottom left portion of the graph is known as the third quadrant. In this region, the value of numbers lying on the xaxis is negative while the value of numbers lying on the yaxis is also negative.

Quadrant 4
The bottom right portion of the graph is known as the fourth quadrant. In this region, the value of numbers lying on the xaxis is positive while the value of numbers lying on the yaxis is negative.
Demonstrating Linearity Relation Between X and Y Axis
Consider the following equation
Y = X+1
Now we want to plot it on the x and yaxis. Let’s say we want to plot it for four coordinate pairs. Starting with the value of x from 0 to 3:
X = 0
Y = X+1
Y = 0+1
Y = 1
For x=0, we get coordinate pair (0,1):
X = 1
Y = X+1
Y =1 +1
Y = 2
For x=1, we get coordinate pair (1,2):
X = 2
Y = X+1
Y = 2+1
Y = 3
For x=2, we get coordinate pair (2,3):
X = 3
Y = 3+1
Y = 4
For x=3, we get coordinate pair (3,4):
Now we can see below illustration that there exists a linear relationship between the x and yaxis.
The coordinate pair (0,1) is shown by point A.
The coordinate pair (1,2) is shown by point E.
The coordinate pair (2,3) is shown by point F.
The coordinate pair (3,4) is shown by point G.
An Example of Plotting on an Axis Graph
Consider the following coordinate pairs, (2,3), (3,2), (1,2), plot these points on the xaxis and yaxis, and also tell in which quadrant each coordinate pair lies. Write abscissa and ordinate each coordinate pair.
Solution
Let (2,3) be the first coordinate pair, decomposing into abscissa and ordinate.
Abscissa = 2
Ordinate = 3
For plotting, We have to move 2 units in a horizontal direction towards the right while we have to move 3 units in a vertical direction upward with respect to the reference point that origin.
As x is positive and y is also positive so the point will lie in the first quadrant as we have seen previously that xaxis and yaxis are positive in the first quadrant. The illustration is shown in the above figure.
Let (3,2) be the second coordinate pair, decomposing into abscissa and ordinate.
Abscissa = 3
Ordinate = 2
For plotting, We have to move 3 units in a horizontal direction towards the left while we have to move 2 units in a vertical direction upward with respect to the reference point that origin.
As x is negative and y is positive so the point will lie in the second quadrant as we have seen previously the xaxis is negative and the yaxis is positive in the second quadrant. The illustration is shown in the above figure.
Let (1,2) be the third coordinate pair, decomposing into abscissa and ordinate.
Abscissa = 1
Ordinate = 2
For plotting, We have to move 1 unit in a horizontal direction towards the left while we have to move 2 units in a vertical direction downward with respect to the reference point that origin.
As x is negative and y is negative so the point will lie in the third quadrant as we have seen previously the xaxis and yaxis are negative in the third quadrant. The illustration is shown in the above figure.
All mathematical drawings and images were created with GeoGebra.