# Equation of a Line Parallel to X-Axis – Definition, Examples | How to find Equation of a Parallel Line?

We have infinite points in the coordinate plane. A line passes through a point (x, y). The different forms of equations of straight lines are equations of horizontal and vertical lines, Point-slope form, two-point form, slope-intercept form, intercept form, and normal form. Get to know more about the Equation of a Line Parallel to the x-axis in the following sections of this page.

## Equation of a Line Parallel to X-Axis

A line can be defined as a straight one-dimensional geometric figure that doesn’t have the thickness and extends endlessly in both directions. A straight line on the coordinate plane can be described by an equation is called the equation of a line. If all the points the straight line having the same y-coordinate or ordinate values, then it is called the equation of a line parallel to the x-axis.

The general form of the equation of a line that is parallel to the x-ais is y = k. Here, k is the distance between the x-axis and the line. If a point P(x, y) lies on the line, then y = b. The equation of x-ais is y = 0 as the x-axis is parallel to itself at a distance of 0 from it.

### Different Forms of the Equation of Line

The various forms of the equations of a straight line are long the lines.

Slope Intercept Form

The equation of a slope-intercept form of a straight line is y = mx + b.

Here, m is the slope,

b is the y-intercept.

Point Slope Form

The point-slope form of a line is y – y₁ = m(x – x₁)

Here, m is the slope of the line

(x₁, y₁) is a point on the line.

Two Point Form

The two points form of a line is $$\frac { y – y₁ }{ y₂ – y₁ } = \frac { x – x₁ }{ x₂ – x₁ }$$

Here, (x₁, y₁), (x₂, y₂) are the two points on the line

Slope of the line = $$\frac { y₂ – y₁ }{ x₂ – x₁ }$$

Intercept Form

Intercept form of a line is $$\frac { x }{ a } +\frac { y }{ b }$$ = 1

Here, a is the x-intercept

b is the y-intercept

Equation of x-axis

The equation of x-axis is y = 0. Because the value of “ordinate” in all the points on the x-axis is zero.

Equation of y-axis

The equation of y-axis is x = 0. Why because the value of abscissa in all points on the y-axis is zero.

General Equation

The general equation of a straight line is ax + by + c = 0.

### Equation of a Line Parallel to X-Axis Examples

Example 1:

Find the equation of a line parallel to the x-axis at a distance of 7 units above the x-axis?

Solution:

We know that the equation of a line parallel to the x-axis at a distance b from it is y = b.

Therefore, the equation of a straight line parallel to the x-axis at a distance 7 units above the x-axis is y = 7.

Example 2:

Find the equation of a line parallel to the x-axis at a distance of 5 units below the x-axis?

Solution:

We know that If a straight line is parallel and below to x-axis at a distance b, then its equation is y = -b.

Therefore, the equation of a line parallel to the x-axis at a distance of 5 units below the x-axis is y = -5.

Example 3:

Find the equation of a straight line parallel to the x-axis at a distance of 10 units above the x-axis?

Solution:

We know that the equation of a line parallel to the x-axis at a distance b from it is y = b.

Therefore, the equation of a straight line parallel to the x-axis at a distance 10 units above the x-axis is y = 10.

### FAQs on Equation of Line Parallel to X-Axis

1. How do you find the equation of a line?

The general form of equation of a line is ax + by + c = 0. Any equation in this form is called the equation of a straight line.

2. What is the equation of the line parallel to the x-axis?

The equation of a straight line parallel to the x-axis is y = b as all the points on that line have y-coordinate values as zero’s. Here, b is the distance between the line and the x-axis.

3. How do you write an equation of a line parallel to a line?

The slope-intercept form of a line is y = mx + c. If two lines are parallel, then their slopes are equal and the y-intercept depends on the line points. So, if you know one line, then it is easy to find the equation of a line parallel to the given line and passes through one point.

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