X axis and Y axis in Graph: Definition, Equation & Examples (2024)

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,
  

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 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. Equation of x-axis is y=0. 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,

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,

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.