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- X and Y Axis in Graph – Definition with Examples
Created on Jan 12, 2024
Updated on January 13, 2024
Table of Contents
The x and y axis are part of the Cartesian coordinate system. The system uses a Cartesian plane to uniquely specify a point by using a pair of real numbers called coordinates. The coordinates are signed distances from two fixed perpendicular lines called coordinate lines. So, the x and y-axis are the coordinate lines on a Cartesian plane. The word Cartesian was adopted from the mathematician Rene Descartes. It is a plane with a rectangular coordinate system that associates each point to a certain pair of numbers.
The pair of numbers can be ordered where the coordinate value of the x-axis comes before the coordinate value of the y-axis. These values can be easily understood after plotting the x and y axis on a graph. Below is more information to help you understand the x and y-axis.
X and Y-Axis Definition
In a two-dimensional space, the x-axis is the horizontal axis, while the y-axis is the vertical axis. The x axis and y axis are represented by two number lines that intersect perpendicularly at the origin to form a coordinate plane. The x-axis is also called the abscissa and the y-axis – the ordinate. Any point on the coordinate plane can be located and represented in the form (x, y) where x is the location of the point in respect to the x-axis and y is the point’s location in respect to the y-axis. The origin point where the y and x axis intersect is represented as (0,0) and is known as the graph origin. Below is the origin and x and y axis labeled.
Plotting Points on X and Y Axis Graph
A point on the coordinate graph can be identified by a pair of numbers representing the location of the point in the x and y-axis. While plotting a single point on the x and y axis graph, we follow the given pair of coordinates representing the distance from the y axis and x axis. The coordinates are written in parentheses starting with the x-axis coordinate and then the y-axis coordinate. For a point (3,2), 3 is the distance of the point from the x-axis and 2 is the distance from the y- axis. This type of coordinate is called an ordered pair. Any other point is plotted the same to either create a curve or a straight line going through the points.
The example of plotting points (1,2), (2,4), and (6,3) is shown below
X and Y-Axis Equation
The two coordinates of a point represent the variables x and y in a linear equation. The standard equation of a straight line is ax+ by+c=0 . Using this equation, we can find different coordinates of x and y and plot them on a graph. From the graph, we can form different equations for different types of straight lines on a coordinate plane .
The equation of the x-axis line
This equation always takes the coordinate value of y as 0 and a varying value of x.
Equation y=0.
The examples are (2,0), (4,0), (7,0), (1,0), (10, 0).
The equation of the y-axis line
Unlike the equation of x-axis, the equation of the y-axis has the coordinate value of x as 0 and a varying value of y.
Equation x=0.
The examples are (0,1), (0,5), (0,3), (0,7), (0,2).
For y=a, the straight line formed is perpendicular to the x-axis, and for x=a the straight line formed is perpendicular to the y-axis y=a, where a is a constant variable
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x=a, where a is a constant coordinate value for x
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The graph of x and y-axis where y=x, the straight line formed cuts across through the origin
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What Comes First: X-Axis or Y-Axis?
The x and y-axis coordinates are values written as an ordered pair (x,y). The first value x represents the point’s location or distance from the x-axis, and the second value y represents the distance from the y-axis. This shows that the x-axis always comes before the y-axis while you plot the points on the graph.
For example, points (3,4) and (4,3) are two different points on the coordinate plane.
Representing a Linear Equation on X and Y Axis
A linear equation is an algebraic algorithm where each term has an exponent of 1, and when graphed, it always results in a straight line. The linear equation is also known as the one-degree equation because the highest power of the variable is always 1. For a nonlinear equation, the power of the variables exceeds 1. The standard form of linear equation for two variables is Ax+ By =C, and for one variable it is Ax+B=0. A is a coefficient and B is a constant for one variable, while for two variables, A and B are coefficients and B is a constant.
Linear equation can also be expressed in the form of slope intercept y=mx+c where m is the slope and c is the y-intercept. The slope is the amount by which the slope is rising or falling. The slope can be calculated by taking two points on the line, for example, (3,4) (5,6), subtracting the x-axis values and the y-axis values, and then dividing the result of the y-axis by the result of the x-axis coordinates.
Coordinates (3,4) (5,6)
X-axis coordinates 5-3=2 6-4=35-3=2= 1.5 is the c( y-intercept) of
Y-axis coordinates 6-4=3 the equation
X and Y Axis Examples
Example 1
Plot the graph of the equation y=x+1 .
To plot a graph, we need the x and y-axis coordinates. Using the equation, we can determine the plot location on the y-axis using random values from the x-axis
y=x+1
Example 2
Fill in the table below to find the y coordinates using the equation y=2x+4.
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What is the standard form of the x and y-axis on a linear equation for two variables?
- y=mx+c
- Ax+By=C
- Ax+B=0
Which of the following equations is not a linear equation?
- y=2×2+4
- y=x+5
- y=3x+1
- y=5x+6
The point (0,3) will lie on the
- Y-axis
- X-axis
- Origin
Conclusion
The result of a linear equation remains unaffected when the same number is added, subtracted, multiplied, or divided on both sides of the equation.This is visible when you chart x and y axis on a coordinate plane since the line will remain a straight line. Otherwise, if the value is added, subtracted, divided, or multiplied on only one side of the equation, it is possible to have a curved graph or points which do not form a straight line. The value of the variable that makes a linear equation true is called the solution or root of a linear equation. In a bar graph x and y axis also form the horizontal and vertical lines respectively.
Frequently Asked Questions
What are the 4 quadrants in a graph?
Quadrant 1: The x-axis and the y-axis coordinates are both positive.
Quadrant 2: The x-axis coordinates are negative, while the y coordinates are positive.
Quadrant 3: The x coordinates and the y coordinates are negative.
Quadrant 4. The x coordinates are positive, while the y coordinates are negative.
The quadrants are counted clockwise starting from the top right.
How do I graph an equation?
You should graph an equation by solving for the coordinates of both y and x, then plotting the points on the graph starting with the x-axis, and then joining the points together to determine if it is a straight line. If it is a straight line, you have solved the equation.
Which point is on the negative y-axis?
A point which lies on the negative y-axis has the coordinates (0,y). This means that the x ordinate must always be zero. Regardless of whether the y coordinate is positive or not, the point will always lie on the negative side of the y-axis. For example, (0,-5), (0,9).
Which is x and y-axis?
The x-axis is the horizontal number line, and the y-axis is the vertical line in a graph. They intersect perpendicularly to form a coordinate plane.
How do you plot a graph with the x and y-axis?
You first draw the number line and label the x and y-axis. Then, plot the coordinates starting with x-axis and then the ordinate of the given variable functions. Connect the coordinate points and plot the graph of a function.
