[Maths Class Notes] on Vertical Line Pdf for Exam

The line is long but not wide. A line is a two-dimensional geometric figure that can move in either direction. A line is made up of an infinite number of points. It is infinite and has no beginnings or endings on either side. A line has only one dimension. Ancient mathematicians introduced the concept of line or straight line in geometry to represent straight objects with negligible width and depth. It’s frequently described in terms of two points.

In the concept of analytic geometry, a line in the plane is often defined as the set of points whose coordinates satisfy a given linear equation, whereas in the concept of incidence geometry, a line may be an independent object distinct from the set of points which lie on it.

A Coordinate Plane

A coordinate plane is a plane where two lines intersect each other at 90o. The horizontal line is known as the x-axis and the vertical line is known as the y-axis. Together the lines are called axes and the point where the two lines intersect each other is known as the origin. There are four quadrants (I, II, III, IV). These quadrants are formed due to axes.


Parallel Lines in the Coordinate Plane:

Parallel lines are those lines which never intersect each other  as shown in the figure.


Perpendicular Lines in the Coordinate Plane:

Perpendicular lines are those lines which intersect each other at a right angle.      


The graph is a design that shows the relation between the variables, quantities, etc. The graph is a collection of points called vertices, and lines between those points are called edges.

Vertical Lines:

The vertical line in coordinate geometry is a line that goes up to down. In other words, the line that is parallel to the y-axis and has the same x coordinate point is vertical. A vertical line can only be drawn when the line has the same x coordinate.

The slope of the vertical line is zero.

The equation of the vertical line is given as 

x = a


x = coordinates of any point on the line

a = point where the line crosses the x-axis 

Hence, it can be seen that the equation is independent of y.

Equation of a Vertical Line

The equation of a vertical line is given by x = a, or x = -a, 


x is the x coordinate of any point on the line

a is where the line crosses the x-intercept.

Vertical Line Properties

  • A vertical line in the graph that is parallel to the y-axis has the equation x = a.

  • A vertical line’s slope is infinity or undefined because it lacks a y-intercept and has a zero denominator in the slope formula.

  • In mathematics, we use a vertical line to determine whether the relationship is a function. It is a function if all vertical lines intersect it at least once. This is also referred to as a vertical line test. If a graph has only one output y for each input x, it is considered a function. As a result, a vertical line cannot serve as a function.


The vertical line is a perpendicular to the surface or another line that serves as the base. Vertical lines in coordinate geometry are parallel to the y-axis and generally perpendicular to horizontal lines. A vertical line is always a straight line that runs from top to bottom or top to bottom. Vertical lines are also referred to as standing lines. Vertical lines are typically drawn by connecting the bases of a square or a rectangle.

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