- Books Name
- ABCD CLASSES Mathematics Book
- Publication
- ABCD CLASSES
- Course
- CBSE Class 9
- Subject
- Mathmatics
Equations of lines parallel to X-axis and Y-axis
In two-dimensional coordinate geometry, the coordinate plane is made up of two axes, namely x-axis and y-axis. The horizontal line in the cartesian plane is called x-axis and the vertical line in the cartesian plane is called y-axis. In this article we are going to learn the equations of line parallel to x-axis and y-axis with a complete explanation and many solved examples.
Equations of Line Parallel to X-axis
We know that the equation of x-axis is y=0.
Thus, the equation of line parallel to the x-axis is given by the equation: y = k.
Where “k” is a constant value.
The above equation is considered as the generalized form of line equation parallel to the x-axis.
We can also say that “k” is a real number, and it is the distance from the x-axis to the line y=k.
An example of a line equation parallel to the x-axis is y=5. It can also be written as y-5 =0.
Equations of Line Parallel to Y-axis
The general form of the equation of y-axis is x = 0.
Hence, the equation of line parallel to the y-axis is given by the equation: x = k.
Where “k” is a constant value, which is a real number that represents the distance from the y-axis to the line x =k.
The equation x = k is the generalized form of line equation parallel to y-axis.
An example of an equation of line parallel to the y-axis x = 7, which can also be represented as x – 7 =0.
Equations of Line Parallel to X-axis and Y-axis Examples
Example 1:
Determine the line equation which is parallel to the x-axis at a distance of 5 units above the x-axis.
Solution:
The equation of the straight line parallel to the x-axis is y = k.
Since the distance is 5 units above the x-axis, the value of k is positive.
Thus, the equation of the straight line parallel to the x-axis at a distance of 5 units above the x-axis is y=5.
The above equation can also be written as y-5 =0.
Example 2:
Find the line equation which is parallel to the y-axis at a distance of 10 units right to the y-axis.
Solution:
The equation of the straight line parallel to the y-axis is x = k.
Since the distance is 10 units right to the y-axis, the value of k is positive.
Therefore, the equation of the straight line parallel to the y-axis at a distance of 10 units right to the y-axis is x = 10.
The line equation x =10 can also be written as x -10 = 0.
What is the equation of the x-axis?
The equation of x-axis is y = 0.
What is the equation of the y-axis?
The equation of y-axis is x = 0.
What is the equation of line parallel to the x-axis?
The equation of a line parallel to x-axis y=k, where “k” is a real number.
Equations of lines parallel to X-axis and Y-axis
In two-dimensional coordinate geometry, the coordinate plane is made up of two axes, namely x-axis and y-axis. The horizontal line in the cartesian plane is called x-axis and the vertical line in the cartesian plane is called y-axis. In this article we are going to learn the equations of line parallel to x-axis and y-axis with a complete explanation and many solved examples.
Equations of Line Parallel to X-axis
We know that the equation of x-axis is y=0.
Thus, the equation of line parallel to the x-axis is given by the equation: y = k.
Where “k” is a constant value.
The above equation is considered as the generalized form of line equation parallel to the x-axis.
We can also say that “k” is a real number, and it is the distance from the x-axis to the line y=k.
An example of a line equation parallel to the x-axis is y=5. It can also be written as y-5 =0.
Equations of Line Parallel to Y-axis
The general form of the equation of y-axis is x = 0.
Hence, the equation of line parallel to the y-axis is given by the equation: x = k.
Where “k” is a constant value, which is a real number that represents the distance from the y-axis to the line x =k.
The equation x = k is the generalized form of line equation parallel to y-axis.
An example of an equation of line parallel to the y-axis x = 7, which can also be represented as x – 7 =0.
Equations of Line Parallel to X-axis and Y-axis Examples
Example 1:
Determine the line equation which is parallel to the x-axis at a distance of 5 units above the x-axis.
Solution:
The equation of the straight line parallel to the x-axis is y = k.
Since the distance is 5 units above the x-axis, the value of k is positive.
Thus, the equation of the straight line parallel to the x-axis at a distance of 5 units above the x-axis is y=5.
The above equation can also be written as y-5 =0.
Example 2:
Find the line equation which is parallel to the y-axis at a distance of 10 units right to the y-axis.
Solution:
The equation of the straight line parallel to the y-axis is x = k.
Since the distance is 10 units right to the y-axis, the value of k is positive.
Therefore, the equation of the straight line parallel to the y-axis at a distance of 10 units right to the y-axis is x = 10.
The line equation x =10 can also be written as x -10 = 0.
What is the equation of the x-axis?
The equation of x-axis is y = 0.
What is the equation of the y-axis?
The equation of y-axis is x = 0.
What is the equation of line parallel to the x-axis?
The equation of a line parallel to x-axis y=k, where “k” is a real number.