**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 .

**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 t****he 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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