X-Axis and Y-Axis in Graph Definition, Equation & Examples

The X-axis and Y-axis are two straight lines that cross each other at a right angle (90°) on a graph.

• The X-axis goes left to right (horizontal).
• The Y-axis goes up and down (vertical).

They are part of the Cartesian Coordinate System, which helps us locate points on a graph.
The point where they intersect is called the origin, and its coordinates are (0, 0).

This system is very useful in math because it helps us draw and understand points, lines, and shapes, and it's a basic idea used in geometry and algebra. Knowing how to read and use the X and Y axes is very helpful in learning graph-related topics.

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Cartesian Coordinate System: A Cartesian Coordinate System consists of two perpendicular lines called the coordinate axes. The horizontal line is the x-axis while the vertical axis is the y-axis. In the following figure,

• the horizontal line marked ‘X’ is the x-axis,
• the vertical lines marked as ‘Y’ is the y-axis
• The point of intersection of the two axes is called the origin and is marked as ‘O’.
• The points marked as (1,3), (3,-2), (-3,1), and (-2,-2) are called the coordinates of those points respectively.

Ordered Pair (Coordinates of a Point)

An ordered pair is a pair of numbers written within brackets and separated by a comma. For example (x,y), where the x-axis and y-axis are any numerical values (positive or negative). Let (x,y) be the coordinates of a point A on the coordinate plane given below, then:

• The first number ‘x’ is called the x-coordinate (or abscissa)
• The second number ‘y’ is called the y-coordinate (or ordinate)
• (x,y) is called the coordinates of point A lying on this coordinate plane.

We can draw a line by joining two or more points on a coordinate plane to form a line segment.

What is x axis and y axis?

The x-axis and y-axis are the axes practiced in coordinate systems. They together form a coordinate plane. The horizontal axis signifies the x-axis and the vertical axis denotes the y-axis.

The location where the x-axis and y-axis meet is identified as the origin and is accepted as the reference point for the plane. The x-axis is also identified as abscissa and the y-axis is also recognized as ordinate.

Any location on the coordinate plane is well described by an ordered pair where the ordered pair is formulated as (x-coordinate,y-coordinate) or (x,y), where the x-coordinate depicts a point on the x-axis or perpendicular length from the y-axis and y-coordinate depicts a point on the y-axis or the perpendicular length from the x-axis

Collinear Points: If two or more points on a coordinate plane lie on the same straight line, then those points are called collinear points.

The X-axis is a horizontal line on the graph that goes from left to right. It starts from the origin (0, 0).

• The part to the right of the origin is called the positive X-axis (+X).
• The part to the left of the origin is called the negative X-axis (–X).

This line helps divide the graph into two halves and is used to locate points in different directions.

Points on the X-Axis

Any point that lies on the X-axis always has a Y-coordinate of 0, since it is exactly on the horizontal line.
Points are written like this: (x, 0), where x can be positive or negative, depending on which side of the origin it is.

Examples:

• (4, 0) is on the positive X-axis
• (–3, 0) is on the negative X-axis

Equation of the X-Axis

The equation of the X-axis is: y=0

This tells us that all points lying on the X-axis have y = 0, no matter what the value of x is.

Positive and Negative Y-Axis

The Y-axis is a vertical line on a graph that starts from the origin (0, 0) and goes up and down.

• The part above the origin is called the positive Y-axis (+Y).
• The part below the origin is called the negative Y-axis (–Y).

We usually think of up as positive and down as negative on the Y-axis.

Points on the Y-Axis

All points that lie on the Y-axis have an X-coordinate of 0, since they are exactly on the vertical line.
These points are written in the form: (0, y), where y can be any positive or negative number.

Examples:

• (0, 3) lies on the positive Y-axis
• (0, –2) lies on the negative Y-axis

Equation of the Y-Axis

The equation of the Y-axis is: x=0

This means that every point on the Y-axis has x = 0, no matter what the y-value is.

Plotting of Points on x axis and y axis

To determine any point on the coordinate plane, we apply an ordered pair where the ordered pair is formulated as (x-coordinate,y-coordinate)/(x,y). Here the x-coordinate denotes a point on the x-axes which is the perpendicular distance from the y-axes and the y-coordinate denotes a point on the y-axes that is the perpendicular distance from the x-axes, therefore it is obvious from above that x-axis comes first when addressing the ordered pair to locate a point.

We can observe in the below diagram that the location of the point on the graph is marked as an ordered pair where the x-axis or x-coordinate leads the y-axes/y-coordinate.

Let the point P lying on a coordinate plane have the coordinates- P(-3,2). Here the x-coordinate(abscissa) is -3 and the y-coordinate (ordinate) is 2.

Hence, x= -3 and y=2.

In the following figure,

• We first take the x-axis and move 3 units along OX’ (on the left side of the x-axis because the abscissa is negative).
• Then we take the y-axis and move 2 units along OY (towards the top because the ordinate is positive), as shown in the graph below,

Axes and Quadrants of the Cartesian Plane

In a Cartesian Plane, there are two main lines:

• The X-axis (goes left and right)
• The Y-axis (goes up and down)

These two lines meet at the origin (0, 0) and divide the plane into four parts, called quadrants.

The Four Quadrants and Their Signs

• Quadrant I:

1. 1. • X is positive
      • Y is positive
      • Example: (3, 4)

• Quadrant II:

1. 1. • X is negative
      • Y is positive
      • Example: (–2, 5)

• Quadrant III:

1. 1. • X is negative
      • Y is negative
      • Example: (–4, –3)

• Quadrant IV:

1. • X is positive
   • Y is negative
   • Example: (6, –2)

Quadrants and Sign Conventions in X axis and Y axis

The x-axes and the y-axes are drawn perpendicular to each other on a coordinate plane. Hence the two axes divide the coordinate plane into four parts. Each part is called a quadrant. Each quadrant has a unique sign convention. This means that the coordinates of a point lying in a coordinate plane have signs (positive or negative) based on the quadrant they lie in.

Look at the following figure,

According to the above figure,

1. The top right part is the first quadrant in which both x and y coordinates are positive.
2. The top left part is the second quadrant in which the x-coordinate is negative and the y-coordinate is positive.
3. The bottom left part is the third quadrant in which both x and y coordinates are negative.
4. The bottom right part is the fourth quadrant in which the x-coordinate is positive and the y-coordinate is negative.

Graphs of Straight Lines (Equation of X axis and Y axis)

The two coordinates of a point on a coordinate plane represent the x and the y variable in a linear equation in two variables of the form ax+by+c=0. This is the standard equation of a straight line. Hence, you can use different values of the variables x y-axes to form coordinates of different points on a coordinate plane, and then join all those points to form a straight line.

Following are the equations for different types of straight lines on a coordinate plane:

1. The equation of x-axis is y=0. The equation of y-axis is x=0.
2. For x= a, the graph is a straight line parallel to y-axis, as given below,

1. For y= a, the graph is a straight line parallel to x-axis, as given below,

1. For y=x, take at least three points to form a straight line. For example if x= -1then y= -1, similarly if x=0 then y=0

So make a table for three values (you can take more values according to the necessity) of x and y as the following,

x	-1	0	1
y	-1	0	1

The graph of y=x is a bisector of the ∠XOY and ∠X’ OY’ and it goes through the origin O, as given below,

1. For y=mx+c, we will again take at least three points. To find the coordinates of these three values of x and put them in the equation to find the corresponding values of y. For example, if the equation of the line is 2x+y=3.

So, y=3-2x, now if we take x=0 then y=3. For x=1, y=1 and for x=2, y= -1So the following table is formed,

x	0	1	2
y	3	1	-1

Now plot these coordinates as points on the graph, as given below,

X-Intercept and Y-Intercept: The x-intercept is a location where a graph intercepts the x-axis. Similarly, the y-intercept is a location where a graph intercepts the y-axis. The y-coordinate of an x-intercept is always zero, and the x-coordinate of a y-intercept is always zero.

For the above graph, filling in x = 0 will return the y-intercept and filling in y = 0 will generate the x-intercept.

Dependent and Independent Axis: For any data set that we are going to graph, the first thing we need to decide is which of the two variables we are going to place on the x-axis and which one on the y-axis. In graphing language, the independent variable is plotted on the x-axis and the dependent variable is plotted on the y-axis respectively.

Important Points on X-axis and Y-axis

• The coordinates of the Origin O are (0,0)
• If a point lies on the x-axis, then the y-coordinate(ordinate) of that point is 0. This means if a point A lies on the x-axis then coordinates of A are (x,0)
• If a point lies on the y-axis, then the x-coordinate(abscissa) of that point is 0. This means if a point B lies on the y-axis then the coordinates of B are (0,y)
• The arrows at both ends of the x-axis and y-axis suggest that both lines are endless.

Solved Examples of X axis and Y axis

Example 1: Plot the given points on a graph, and check whether they lie on a straight line or not.

(5, 0), (-4.5, 0) and (3, 0).

Solution: Let us plot the given points A(5, 0), B(-4.5, 0), and C(3, 0).

Yes, all the points are on the same line, i.e. x-axis.

Example 2: Plot the two points (2, 3) and (3, 2) on graph paper and find the point where the straight line meets the x-axis.

Solution: Let us plot the two points on a graph.

On extending the line and making it meet the x-axis, we get that the straight line formed by joining the points (2, 3), and (3, 2), meet x-axis at (5, 0).

Example 3: Find the point where the straight line y = 2x + 6 meets the y-axis.

Solution: We know that for a line to meet the y-axis, the x-coordinate needs to be zero. So, we can find the point of intersection of the given line and the y-axis, by simply putting the value of x in the given equation.

y = 2x + 6, putting x = 0;

y = 2(0) + 6 = 6

So, we can say that the straight line y = 2x + 6, meets the y-axis at (0, 6).

Hope you have understood all the concepts regarding the X axis and Y axis stated in this article. If you have any questions or suggestions for us then you can contact us directly. Also, you can download the Testbook App, and kickstart your preparations for any competitive exam NOW!

If you are checking X axis and Y axis article, also check related maths articles:
Scatter Plot	Radical Axis
Direction Cosines	Straight Line
Area Between Two Curves	Latus Rectum of Hyperbola

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