Vertical Line

Introduction :

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. From the figure, it can be seen that they are moving in a counterclockwise direction from the upper right.     


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.      

Graph :

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

Where,

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.

The basic difference between the horizontal and vertical line has been depicted below.


Properties of Vertical Lines:

  • Since the line does not cross the y-axis, the equation of the vertical line does not have a y-intercept.

  • The denominator of the slope is zero. Therefore, the slope is undefined.

  • The equation of a vertical line always takes a form x=k.

  • The vertical line is used to check whether the related functions in math


How do you Graph a Vertical Line?

The vertical lines are the lines that go straight up and down. Vertical lines go from a given point on x plane. So to draw a vertical line a point on the x plane is drawn and then a line from that point is drawn to make a straight line.

Finding the Equation of the Vertical Line :

All lines need a slope. So in case of vertical line slope of the line is given by

m = \[\frac{y2-y1}{x2-x1}\]


Once you do the calculation using this equation you will see that the value of the denominator is zero (0). Therefore the slope of the vertical line is undefined as you can see.

Example:

Determine if the line shown in the figure is vertical and write its equation.

Solution:

The points A and B on the line are at (-15, 3) and (-15, 20). The first coordinate in each pair is the x-coordinate which are -15, and -15. Since they are equal, the line is vertical.

Since the line crosses the x-axis at -15, the equation of the line is

x = -15;

which can be read as "for all values of y, x is -15".

Example:

Determine the equation of the line shown in the figure.

Solution:

Since the line crosses the x-axis at -3. The equation of the line is

 x = -3

Which can be read as ‘for all values of y, x is -3’.


Example:

Draw the plot for the given equation x= 6.

Solution:

The plot has been successfully traced.

Example:

Find the slope of the given coordinate point (6, 2) and (6, 0).

Solution:

This question can be solved as 

Given- y1 = 0

             y2 = 2

x1 = 6

x2 = 6

From the slope formula we get that,

slope = m = \[\frac{2-0}{6-6}\] = \[\frac{2}{0}\]

m = undefined

Hence it can be seen that the slope of the vertical line is undefined.

Example:

Find the slope of the given coordinate point (7, 3) and (7, 0).

Solution:

This question can be solved as 

Given- y1 = 0

             y2 = 3

x1 = 7

x2 = 7

From the slope formula we get that,

slope =  m = \[\frac{3-0}{7-7}\] = \[\frac{3}{0}\]

m = undefined

Hence it can be seen that the slope of the vertical line is undefined.

Example:

Find the slope of the given coordinate point (6, 2) and (2, 8).

Solution:

This question can be solved as 

Given- y1 = 8

             y2 = 2

x1 = 2

x2 = 6

From the slope formula we get that,

slope = m = \[\frac{2-8}{6-2}\] = \[\frac{-3}{2}\] = -1.5

m = defined

Hence it can be seen that the slope of the vertical line is defined.

Example:

Find the slope of the given coordinate point (0, 6) and (6, 0).

Solution:

This question can be solved as 

Given-  y1 = 6

              y2 = 0

x1 = 6

x2 = 0

From the slope formula we get that,

slope = m =\[\frac{0-6}{0-6}\] = \[\frac{-6}{-6}\]= -1

m = defined

Hence it can be seen that the slope of line is defined that is -1

Test Yourself:

  1. Find the slope, having coordinate points (7, 10) and (7, 15). And also draw the graph.

  2. Draw the graph of the equation x- 23 = 0.

  3. An equation is given 2x + 15= 0. Draw the graph of the given equation.

  4. (10, 5) and (6, 7) are the coordinate of a line, find the slope and draw the graph of the given point.

  5. (0, 5) and (0, 7) are the coordinate of a line, find the slope and draw the graph of the given point.

  6. (10, 4) and (10, 7) are the coordinate of a line, find the slope and draw the graph of the given point.

  7. (10, 7) and (7, 7) are the coordinate of a line, find the slope and draw the graph of the given point.

  8.  (2, 5) and (1, 7) are the coordinate of a line, find the slope and draw the graph of the given point.

  9. (10, 7) and (2, 7) are the coordinate of a line, find the slope and draw the graph of the given point.