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.

Table of Contents:

• Equation of Line Parallel to X-axis
• Equation of Line Parallel to Y-axis
• Solved Examples
• Practice Problems
• FAQs

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.

Practice Problems

1. Find the equation of line parallel to the x-axis such that the distance of 7 units down to the x-axis.
2. Determine the equation of line parallel to the y-axis such that the distance of 4 units left to the y-axis.

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