We will learn how to find the equation of y-axis and equation of a line parallel to y-axis.

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

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

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

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

Or

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

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

If a straight line is parallel and to the left of x-axis at a distance a, then its equation is x = -a.

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

**1.** Find the
equation of a straight line parallel to y-axis at a distance of 3 units on the
left hand side of y-axis.

**Solution:**

We know that the equation of a straight line is parallel and to the left of x-axis at a distance a, then its equation is x = -a.

Therefore, the equation of a straight line parallel to y-axis at a distance of 3 units on the left hand side of y-axis is x = -3

**2.** Find the equation of a straight line parallel to y-axis
at a distance of 20 units on the right hand side of y-axis.

**Solution:**

We know that the equation of a straight line is parallel and to the right of x-axis at a distance a, then its equation is x = a.

Therefore, the equation of a straight line parallel to y-axis at a distance of 20 units on the right hand side of y-axis is x = 20

**●**** 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**

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