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Equation of Line Parallel to Y Axis
The equation of a line parallel to y axis is of the form x = a and it cuts the xaxis at the point (a, 0). This line is parallel to y axis and is at a perpendicular distance of 'a' units from the yaxis. 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 xaxis at the point (a, 0). Here all the points on this line parallel to the yaxis will have the same x coordinate of a. Further the equation of line parallel to yaxis and cutting the xaxis at point (a, 0) is at a perpendicular distance of 'a' units from the yaxis. The distance between two lines which is a line parallel to yaxis and the yaxis is a units. This equation of line parallel to y axis makes an angle of 90º with the xaxis, 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 xaxis passes through the first and the fourth quadrant. And the equation of line parallel to the y axis and cutting the negative xaxis passes through the second and the third quadrant of the coordinate axes.
As an example, let us consider the equation of line parallel to yaxis, which is x = 3. This equation x = 3 cuts the xaxis 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 yaxis
 The line parallel to yaxis cuts the xaxis at one distinct point.
 The line parallel to the yaxis cuts the xaxis at only one point (a, 0) and has the equation x = a.
 The equation of line parallel to yaxis and cutting the xaxis at the point (a, 0) is at a perpendicular distance of 'a' units from the yaxis.
 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 yaxis is undefined.
 The line parallel to the yaxis is always perpendicular to the xaxis.
 There can be numerous lines drawn parallel to the yaxis.
 The equation of line parallel to yaxis does not have the y variable.
Related Topics
The following topics are helpful to find the equation of line parallel to yaxis.
Examples on Equation of Line Parallel to Y Axis

Example 1: Find the equation of line parallel to yaxis and passing through the point (4, 5).
Solution:
The given coordinates of the point is (4, 5).
The line parallel to yaxis and passing through this point(4, 5) cuts the xaxis at the point (4, 0)
Hence the equation of line parallel to the y axis is x = 4.

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 xintercept of this line is 5, and it cuts the xaxis at the point (5, 0).
The required equation of line parallel to the yaxis having this above line also passes through the point (5, 0).
Therefore, the equation of line parallel to yaxis and passing through the point (5, 0) is x = 5.
FAQs on Equation of Line Parallel to Y Axis
What Is 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 xaxis at the point (a, 0). This equation of a line x = a is a line parallel to yaxis and is at a perpendicular distance of 'a' units from the yaxis. And every point on this line x = a has the value of x coordinate equal to 'a'.
What Is the Equation of YAxis?
The equation of yaxis is the line which cuts the xaxis at the origin, (0, 0). Hence the equation of a yaxis 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 xaxis at the point (a, 0). This can be taken as the formula for equation of a line parallel to y axis.
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