X and Y Axis: Equation and Examples

X and Y Axis - The X and Y axes are the core concepts for drawing graphs representing two variables and their relationships through an effective pictorial form. Suppose you want to know how your height increases with age; use the x-axis and y-axis to plot these two values and get an amazing growth curve! 

For presenting and interpreting medical, scientific, or economic data, the x and y axis becomes a handy tool. This blog explains what the x and y axes are and their functions, and provides simple x and y-axis graph examples. You can understand how these horizontal and vertical lines provide a framework for graphical interpretation and decision-making.

Also read:  Profit and loss formula

What Are the X and Y Axis?

The x and y axis are two perpendicular lines that form the basis of drawing a graph. They are the main two lines in the cartesian coordinate plane, which are used as references to locate points, plot graphs, and represent relationships between variables in two dimensions.

• X-axis: It is the horizontal line that runs left to right.

• Y-axis: It is the vertical line that runs up and down.

The x-axis is also called the abscissa, and the y-axis is called the ordinate.

These two lines intersect at a point called the origin.

Also read: Difference between 2D and 3D shapes

Where Are the X Axis and Y Axis on a Graph?

In the cartesian plane, the X-axis is the horizontal line that divides the area into two equal parts: top and bottom. Similarly, the Y-axis is the vertical line that divides the area into two equal parts: left and right. These number lines help find the values while plotting a graph. These two lines meet at the origin for which both the x and y values are zero.

The x-axis and y-axis contain values that are positive as well as negative. Let's explain in detail:

• Positive x-axis: The right-hand side of the origin

• Negative x-axis: The left-hand side of the origin

• Positive y-axis: The upward direction from the origin

• Negative y-axis: The downward direction from the origin

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Plotting Points Using X-axis and Y-axis

The x-axis, and y-axis denote the position of a point on a coordinate plane. Any point is expressed as (x, y) where x is the x-coordinate value and y is the y-coordinate value. The x-coordinate denotes a value on the x-axis, and the y-coordinate denotes a value on the y-axis. Please note the following while looking at the values of x and y:

• Positive x-values increase toward the right.

• Negative x-values extend to the left of the origin.

• Positive y-values go upwards.

• Negative y-values go below the origin.

Also read: Quadrilateral

Quadrants Formed by X-axis and Y-axis

The x and y axes combinedly divide the graph into four quadrants, which are numbered counterclockwise:

• Quadrant I: Contains points with positive x-values and y-values

• Quadrant II: Contains points with negative x-values and positive y-values

• Quadrant III: Contains points with negative x-values and y-values

• Quadrant IV: Contains points with positive x-values and negative y-values

X and Y Axis Graph Example

Let's look at a simple x and y-axis graph example for plotting points.

Suppose you want to plot these points:

• A (1, 3)

• B (−3, 1)

• C (−2, −2)

• D (3, −2)

Follow the below-mentioned steps to place the points:

• Point A (Quadrant I): Go 1 unit to the right on the x-axis from the origin and move 3 units up parallel to the y-axis.

• Point B (Quadrant II): Go 3 units to the left starting from origin and move 1 unit up.

• Point C (Quadrant III): Go 2 units to the left from the origin and move 2 units down parallel to the y-axis.

• Point D (Quadrant IV): Go 3 units to the right from the origin and then 2 units down.

This simple activity helps you understand how points are plotted using the x-axis and y-axis.

How to Write Equations of X Axis and Y Axis

The x-axis and y-axis are straight lines, so they must have equations to represent them. The equation of a straight line going through the origin is y = mx. However,  equations of x and y axes are very straightforward. Let's find out:

Equation of the X-Axis:

On the x-axis, the y-coordinate is always zero because you are moving along the x-axis but not moving up or down.

So, the equation of the x-axis is: y = 0

It means that for any point on the x-axis, the value of the y-coordinate is zero.

Examples of points on the x-axis are (2, 0), (−5, 0), (12, 0), etc.

Equation of the Y-Axis:

On the y-axis, the x-coordinate is always zero because you are only moving up and down but not moving left or right.

So, the equation of the y-axis is: x = 0

It means that for any point on the y-axis, the value of the x-coordinate is zero.

Examples of points on the y-axis are (0, -6), (0, −7), (0, 15), etc.

Also read: Equation: Definition, Types, Examples, Differences

What Is the Purpose of the X and Y Axis?

The x and y axes become useful in pictorial representation and graphic solutions of different mathematical problems. The x-axis and y-axis are used in the following activities:

• Representing relationships between two variables.

• Locating the position of points on a plane

• Draw lines and curves representing equations.

• Interpret data from charts, bar graphs, etc.

• Analyze trends in the fields of physics, economics, or statistics.

X and Y Axis Examples

The concepts of the x and y axes are not just limited to textbooks; they are used in many practical applications where various data types and their inter-relations are represented graphically. It helps in better understanding and decision-making. Here are some examples:

Business Graphs: Companies use graphs to compare profit (y-axis) over time (x-axis).

Science: In physics, graphs represent the relation between two parameters—for example, velocity (y-axis) vs. time (x-axis).

Economics: Trend analysis is done by plotting magnitude against period. For example, GDP can be shown through bar graphs (y-axis) for different years (x-axis).

Computer Graphics: Every visual element on a screen has an x and y position to determine its location.

Medical Charts: Doctors use x and y-axis charts to monitor heart rates, blood pressure, or glucose levels over time.

Also read: What is a Pie Chart?

Drawing a Line on Graph Using X-Axis and Y-Axis

The equation of a straight line is represented as y = mx + c (m and c are constant). If we take different values of x, for each value of x, we get a unique value of y, stratifying the equation. 

We take these x and y values as the x-coordinate of the y-coordinate of points and plot them on the graph using the x and y-axis. When we draw a line through all these points, it gives the graphical representation of the given straight-line y =mx + c

Let's explain with an example. The equation of a line is y= 2x + 1

Now, for different values of x, we get different values of y as follows:

Now, by plotting these points on the graph and joining them, we get a straight line that represents y = 2x +1                   

Also read: Basic Maths Formula    

Important Points About X and Y Axis

• X-axis is horizontal, and the Y-axis is vertical and intersects at the origin.

• The x-coordinate and y-coordinate of origin are (0, 0).

• Origin is the middle point of the X and Y axis.

• There are infinite points on the X and Y axis -both positive and negative.

• The point where a graph meets x -the x-axis is called the x-intercept.

• The point where a graph meets the y-axis is called the y-intercept.

• The X-axis measures the independent variable, and the Y-axis measures the dependent variable.

The x and y axes are important for measuring, representing, and visualizing relationships between variables. Understanding the x-axis and y-axis, practicing with x and y-axis graph examples, and learning how to write the equation of the x-axis and y-axis will help apply them in many practical applications.

Also read:  Angles Meaning and Definition

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