What Is the Equation of the Y-Axis? Definition & Key Facts
To understand the equation of the y-axis. First, we have to understand graphs. What is a graph? A graph consists of a horizontal line and a vertical line, called the horizontal axis and the vertical axis, respectively. Why do we use a graph? A graph is used to represent data. A point can be determined horizontally or vertically, which can be easily understood using a graph. The horizontal axis is called the x-axis and the vertical axis is called the y-axis in a graph. Let us proceed further to know more about this topic.
More about Graphs and X and Y-axis
To represent a point on a graph we take given points on the x-axis and y-axis respectively as (x,y). The (0,0) coordinate is called origin, where the x-axis and the y-axis meet. We take positive points at the x-axis and negative points at the x’-axis. Similarly, we take positive points at the y-axis and negative points at the y’-axis.
A Graph
What Is the Equation of the Y-axis?
Let us have an equation y = 2x + 3. To represent it, we will make a table.
Here we have values for both y and the x-axis. So, what is the equation of the y-axis?
When all the values of the equation lie on the y-axis, the values of x come 0 for all values of y, it is called the equation of the y-axis. So, the equation of y-axis is
x = 0
Let understand it with an example, x = 0*y
For y = 3, x will be 0
Y = -3, x will be 0
Similarly, for all value of y, x is 0.
Graph of the Equation of Y-axis
Line Parallel to Y-axis
A line is said to parallel to the y-axis when it is drawn along the y-axis, hence perpendicular to the x-axis, where the value of x remains constant for all values of y.
The common equation of the line parallel to the y-axis is
x= by + c, where b is 0
So, the equation of the line parallel to the y-axis is x = c. Here c is a constant.
Graph of a Line Parallel to Y-axis
When b is 0, for all values of y, the value of x comes constant c. Let's understand it with an example.
x= (0)y + 2
A Line parallel to the Y-axis
Let’s Write the Equations of the Y-axis and X-axis
From the above discussion, we know the equation of the y-axis is x=0.
Similarly, the equation of the x-axis is y=0.
Here the point lies on the x-axis therefore for all values of x, y becomes 0. So, the equation of the y-axis is given by
x = 0
And the equation of the x-axis is given by
y = 0
Questions for Practice
Draw the points (0,2), (0,4), and (0,-7)on a coordinate system. Do all the points lie on the same line? Can you name the line
(Answer. y-axis)
Draw the points (2,0), (6,0), and (-3,0) on a coordinate system. Do all the points lie on the same line? Can you name the line?
(Answer: x-axis)
Draw the points (3,2), (3,4.5), and (3,-3) on a coordinate system. Do all the points lie on the same line? Can you name the line?
(Answer: yes, a line parallel to the y-axis)
Draw the points (2,2), (0,2), and (6,2) on a coordinate system. Do all the points lie on the same line? Can you name the line?
(Answer: y a line parallel to the x-axis)
Summary
We have learned the coordinates of the graph. The coordinate is written as (x,y).We have learned the equation of the y-axis. The equation is x = 0. We have learned the equation of the x-axis. The equation is y = 0. We have learned the equation of line parallel to the y-axis. The equation of the line parallel to the y-axis is x = c.
FAQs on Equation of the Y-Axis Explained
1. Which equation represents the y-axis?
The equation that represents the y-axis in coordinate geometry is $x = 0$. This is because every point on the y-axis shares the same x-coordinate, which is always zero. The y-value can be any real number.
2. How to solve for the y-axis?
To solve for the y-axis, set $x$ equal to zero in your equation. This helps you find where your graph crosses or interacts with the y-axis. The y-axis equation is always $x = 0$, no matter the value of y.
3. What does the y = mx + c stand for?
$y = mx + c$ is the general equation of a straight line, where $m$ stands for the slope and $c$ is the y-intercept. This form helps you understand how changes in $x$ influence $y$ on a graph.
4. Which axis is y = -1 parallel to?
The line $y = -1$ is parallel to the x-axis. It shows all points where the y-coordinate is -1, regardless of the x-coordinate. Every line of the form $y = k$ (where $k$ is a constant) is parallel to the x-axis.
5. What is the equation of the y-axis in standard form?
In standard form, the equation of the y-axis is written as $x = 0$. This identifies the vertical axis on the Cartesian plane, where all points have the x-coordinate equal to zero and y can be any number.
6. How does the equation x = 0 represent the y-axis?
The equation $x = 0$ matches every point where x is zero, which defines the y-axis. If you plot points where only x is zero, you always get a vertical line running through the origin — the y-axis.
7. Can the equation of y-axis be written using y?
No, the equation of the y-axis is best written as $x = 0$ because the y-axis contains points with any y-value but always x equal to zero. Using $y$ alone does not properly define this vertical line.
8. What kind of line is the y-axis on the coordinate plane?
The y-axis is a vertical line on the coordinate plane. It divides the plane into left and right halves and passes through all points where $x = 0$, making it fundamental in graphing equations.
9. How do you check if a point lies on the y-axis?
To check if a point is on the y-axis, look at its coordinates. If the x-coordinate is zero, the point lies on the y-axis, no matter what the value of y is. For example, (0,5) is on the y-axis.
