# EQUATIONS OF HORIZONTAL AND VERTICAL LINES

## About "Equations of horizontal and vertical lines"

Equations of horizontal and vertical lines :

In a cartesian plane, we can draw two types of lines.

(i) Horizontal line

(ii) Vertical line.

What is horizontal line ?

The line which is parallel to x- axis is known as horizontal line.

In the above graph the line y  = 1 is parallel to x axis, hence it is horizontal line.

Equation of the horizontal line will be in the form y = k

What is vertical line ?

The line which is perpendicular to x-axis is known as vertical line.

In the above graph, the line x = -1 is parallel to y axis, hence it is vertical line.

Equation of the horizontal line will be in the form x = h

What is slope ?

The slope of a line characterizes the direction of a line. To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .

## Slopes of Horizontal and Vertical Lines

Horizontal lines have the following characteristics :

• They have Zero Slope.
• They are drawn from left to right through the y-axis.
• The equation only has one constant to determine where it will be drawn. Such as (y = 5, y = - 3, y = 17, etc.)
• And the points of such equations have the same value for the 'y' on the given points such as {(-2, 4), (9, 4)}, {(3, -7), (-4, -7), (8, -7)}

Horizontal lines have the following characteristics :

• They have an Undefined Slope.
• They are drawn from top to bottom through the x-axis.
• The equation only has one constant to determine where it will be drawn. Such as (x = 1, y = 4, y = -11, etc.)
• And the points of such equations have the same value for the 'x' on the given points such as {(6, -1), (6, 7)}, {(1, 2), (1, -6), (1, 17), (1, 0)}

Let us see some example problems based on the above concepts.

Example 1 :

Write an equation of the line which passes through (0, 4), (10, 4)

Solution :

By considering the above points, the y-coordinate values are same.

Hence it is horizontal line. Its slope must be zero.

Example 2 :

Write an equation of the line which passes through (-4, 1), (-4, 7).

Solution :

By considering the above points, the x-coordinate values are same.

Hence, it is vertical line and it has undefined slope.

Example 3 :

Find the slope of the line y = -3

Solution :

Since the given line is in the form of y = a constant, it remembers the word (HOY). From this we come to know the given line is horizontal line.

Hence its slope is zero.

Example 4 :

Find the slope of the line x = 5

Solution :

Since the given line is in the form of x = a constant, it remembers the word (VUX). From this we come to know that the given line is vertical line.

Hence its slope is undefined.

Example 5 :

What is the equation of a line that passes through the point (3,-5) and has an undefined slope?

Solution :

Since the slope of the line passes which through the point (3, -5) is undefined, it should be vertical line.

This remembers the word "VUX".  So the equation is in the form x = a constant.

Hence equation of the required line is x = 3.

After having gone through the stuff given above, we hope that the students would have understood "Equations of horizontal and vertical lines".

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