To find the equation of x-axis and of a line parallel to x-axis:

Let AB be a straight line parallel to x-axis at a distance b units from it. Then, clearly, all points on the line AB have the same ordinate b. Thus, AB can be considered as the locus of a point at a distance b from x-axis and all points on the line AB satisfy the condition y = b.

Thus, if P(x, y) is any point on AB, then y = b.

Hence, the equation of a straight line parallel to x-axis at
a distance b from it is y = b.

The equation of x-axis is y = 0, since, x-axis is a parallel to itself at a distance 0 from it.

Or

Let P (x,y) be any point on the x-axis. Then clearly, for all position of P we shall the same ordinate 0 or, y = 0.

Therefore, the equation of x-axis is y = 0.

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

Solved examples to find the equation of x-axis and equation of a line parallel to x-axis:

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

**Solution:**

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

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

**2.** Find the equation of a straight line parallel to x-axis
at a distance of 7 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 straight line parallel to x-axis at a distance 7 units below the x-axis is y = -7.

**●**** The Straight Line**

**Straight Line****Slope of a Straight Line****Slope of a Line through Two Given Points****Collinearity of Three Points****Equation of a Line Parallel to x-axis****Equation of a Line Parallel to y-axis****Slope-intercept Form****Point-slope Form****Straight line in Two-point Form****Straight Line in Intercept Form****Straight Line in Normal Form****General Form into Slope-intercept Form****General Form into Intercept Form****General Form into Normal Form****Point of Intersection of Two Lines****Concurrency of Three Lines****Angle between Two Straight Lines****Condition of Parallelism of Lines****Equation of a Line Parallel to a Line****Condition of Perpendicularity of Two Lines****Equation of a Line Perpendicular to a Line****Identical Straight Lines****Position of a Point Relative to a Line****Distance of a Point from a Straight Line****Equations of the Bisectors of the Angles between Two Straight Lines****Bisector of the Angle which Contains the Origin****Straight Line Formulae****Problems on Straight Lines****Word Problems on Straight Lines****Problems on Slope and Intercept**

**11 and 12 Grade Math**

**From Equation of a Line Parallel to x-axis to HOME PAGE**

**Didn't find what you were looking for? Or want to know more information
about Math Only Math.
Use this Google Search to find what you need.**

## New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.