Equations of Lines Parallel to X-axis and Y-axis | Testbook.com

Equations of Line Parallel to X-axis

The equation of the x-axis is y=0. Therefore, any line parallel to the x-axis can be represented by the equation: y = k, where “k” is a constant. This equation represents the general form of a line parallel to the x-axis.

The constant “k” is a real number and signifies the distance from the x-axis to the line y=k. A practical example of such an equation is y=6, which can also be represented as y-6 =0.

Equations of Line Parallel to Y-axis

The general form of the equation of the y-axis is x = 0. Consequently, any line parallel to the y-axis can be represented by the equation: x = k, where “k” is a constant. This equation represents the general form of a line parallel to the y-axis.

The constant “k” is a real number and represents the distance from the y-axis to the line x =k. An example of such an equation is x = 8, which can be represented as x – 8 =0.

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Solved Examples

Example 1:

Find the equation of the line that is parallel to the x-axis and is 7 units above the x-axis.

Solution:

The general equation of a line parallel to the x-axis is y = k. Here, the distance is 7 units above the x-axis, hence the value of k is positive 7. Therefore, the equation of the line is y=7, which can also be written as y-7 =0.

Example 2:

Determine the equation of the line that is parallel to the y-axis and is 12 units to the right of the y-axis.

Solution:

The general equation of a line parallel to the y-axis is x = k. The line is 12 units to the right of the y-axis, hence the value of k is positive 12. Therefore, the equation of the line is x = 12, or x -12 = 0.

Practice Problems

1. Find the equation of a line parallel to the x-axis that is 9 units below the x-axis.
2. Determine the equation of a line parallel to the y-axis that is 5 units to the left of the y-axis.