# Find the Equation of a Line Parallel to Y Axis | Different Forms of Equations of a Straight Line

Equation of a Line Parallel to Y-Axis: As we all aware of the infinite points in the coordinate plane so take an arbitrary point P(x,y) on the XY Plane and a line L. Now, finding the point that lies on the line is a very essential task for bringing an equation of straight lines into the picture in 2-D geometry.

In an equation of a straight line, terms involved in x and y. So, in case, the point P(x,y) meets the equation of the line, then the point P lies on the Line L. Now, you all will come to know about the Equation of a Line Parallel to Y-Axis, how to find it for the given point, and much more like different forms of equations of a straight line in the below modules.

## Find the Equation of a Line Parallel to Y-Axis

Now, we will explain how to find the equation of Y-axis and the equation of a line parallel to Y-axis. By following this explanation, you will understand how easy to calculate and solve the equation of a straight line parallel to Y-axis. So, let’s start with the process of finding an Equation of a Line Parallel to the y-axis.

Let AB be a straight line parallel to the y-axis at some distance assume ‘a’ units from the Y-axis. From the below figure, it is clear that line L is parallel to y-axis and passing through the value ‘a’ on the x-axis. So, the equation of a line parallel to y-axis is X=a.

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

Or

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

### Different Forms of Equations of a Straight Line

In addition to the equation of a line parallel to the y-axis, let’s have a glance at some various forms of the equation of a straight line. Here is the list of different forms of the equation of a straight line:

• Slope intercept form
• Point slope form
• Two-point form
• Intercept form
• Normal form
• Point-slope form

### Worked-out Examples on Equation of y-axis and Equation of a line parallel to the y-axis

1. Write the equation of a line parallel to y-axis and passing through the point (−2,−4).

Solution:

As we know that the Equation of line parallel to y-axis is x=a.

The given point (−2,−4) lies on our required line, so that

⟹ x = -2

Therefore, the equation of the required line is x=−2.

2. Calculate the equation of a straight line parallel to y-axis at a distance of 4 units on the left-hand side of the y-axis.

Solution:

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

Hence, the equation of a straight line parallel to y-axis at a distance of 4 units on the left-hand side of the y-axis is x = -4,

3. Find the equation of a line parallel to the y-axis and passing through the point (5,10)?

Solution:

A line parallel to the y-axis will be of form x=a

Given the line passes through (5,10)

So, x=5

Hence, The equation of a line is x – 5 = 0.

### FAQs on Line Parallel to Y-Axis

1. What is the equation representing Y-axis?

The equation of a line which is representing the y-axis is x=0.

2. How to calculate the equation of a line?

Typically, the equation of a line is addressed as y=mx+b where m is the slope and b is the y-intercept.

3. What is the formula for point-slope form?

The formula for Point-Slope of the line by the definition is, m = $$\frac { y − y1 }{ x − x1 }$$

y − y1 = m(x − x1).