What is the equation of the line parallel to the y-axis and 3 units to the right of the y-axis?

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The equation of a line parallel to y axis is of the form x = a and it cuts the x-axis at the point (a, 0). This line is parallel to y axis and is at a perpendicular distance of 'a' units from the y-axis. The slope of the equation of line parallel to y axis is undefined, since it is inclined at 90º with the x axis.

Let us learn more about how to find the equation of line parallel to y axis, the properties of this line, and check a few examples.

How To Find Equation of Line Parallel to Y Axis?

The equation of line parallel to y axis is of the form x = a, and it cuts the x-axis at the point (a, 0). Here all the points on this line parallel to the y-axis will have the same x coordinate of a. Further the equation of line parallel to y-axis and cutting the x-axis at point (a, 0) is at a perpendicular distance of 'a' units from the y-axis. The distance between two lines which is a line parallel to y-axis and the y-axis is a units. This equation of line parallel to y axis makes an angle of 90º with the x-axis, and hence its slope is equal to the value of Tan90º, which is undefined.

The equation of line parallel to the y axis and cutting the positive x-axis passes through the first and the fourth quadrant. And the equation of line parallel to the y axis and cutting the negative x-axis passes through the second and the third quadrant of the coordinate axes.

As an example, let us consider the equation of line parallel to y-axis, which is x = 3. This equation x = 3 cuts the x-axis on the positive side at the point (3, 0), and it passes through the first and the fourth quadrant. Further, the points (3, 1), (3, 2), (3, 5), (3, -2), (3, -3), (3, -5), all of these points falling on this line x = 3.

Properties of Equation of Line Parallel to Y Axis

The following are the properties of the equation of line parallel to the y-axis

• The line parallel to y-axis cuts the x-axis at one distinct point.
• The line parallel to the y-axis cuts the x-axis at only one point (a, 0) and has the equation x = a.
• The equation of line parallel to y-axis and cutting the x-axis at the point (a, 0) is at a perpendicular distance of 'a' units from the y-axis.
• The x coordinate of all the points lying on the line parallel to the y -axis are all the same value.
• The slope of a line parallel to the y-axis is undefined.
• The line parallel to the y-axis is always perpendicular to the x-axis.
• There can be numerous lines drawn parallel to the y-axis.
• The equation of line parallel to y-axis does not have the y variable.

Related Topics

The following topics are helpful to find the equation of line parallel to y-axis.

Examples on Equation of Line Parallel to Y Axis

1. Example 1: Find the equation of line parallel to y-axis and passing through the point (4, 5).

   Solution:

   The given coordinates of the point is (4, 5).

   The line parallel to y-axis and passing through this point(4, 5) cuts the x-axis at the point (4, 0)

   Hence the equation of line parallel to the y axis is x = 4.

2. Example 2: Find the equation of line parallel to the y axis and has the same intercept as the line 3x + 5y - 15 = 0.

   Solution:

   The given equation of the line is 3x + 5y - 15 = 0

   We need to change this equation into intercept form.

   3x + 5y = 15

   3x/15 + 5y/15 = 1

   x/5 + y/3 = 1

   The x-intercept of this line is 5, and it cuts the x-axis at the point (5, 0).

   The required equation of line parallel to the y-axis having this above line also passes through the point (5, 0).

   Therefore, the equation of line parallel to y-axis and passing through the point (5, 0) is x = 5.

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FAQs on Equation of Line Parallel to Y Axis

The equation of line parallel to y axis is of the form x = a, and it cuts the x-axis at the point (a, 0). This equation of a line x = a is a line parallel to y-axis and is at a perpendicular distance of 'a' units from the y-axis. And every point on this line x = a has the value of x coordinate equal to 'a'.

What Is the Equation of Y-Axis?

The equation of y-axis is the line which cuts the x-axis at the origin, (0, 0). Hence the equation of a y-axis is x = 0.

What Is the Slope of the Equation of Line Parallel to Y Axis?

The slope of the equation of line parallel to y axis is undefined. The line parallel to y axis is at an angle of 90º to the x - axis and the slope of this line is tan90º, which is undefined.

What Is Required to Find Equation of Line Parallel to Y Axis?

The minimum required criterion to find the equation of line parallel to y axis is any point on the line. The equation of line parallel to y axis and passing through a point (a, b) is the x = a.

What Is the Formula to Find Equation of a Line Parallel to Y Axis?

The standard form of the equation of line parallel to y axis is x = a, and it cuts the x-axis at the point (a, 0). This can be taken as the formula for equation of a line parallel to y axis.

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

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The equation of the line parallel to Y axis and 3 units to the right of it, is A. y =3B. y =0C. x=3 D. x =0

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