# Slope (Gradient) Definition

The **slope** is defined as the **ratio** between the **change in height** to the **change in horizontal distance**. In simple words, slope means how steep a line is. It has multiple practical examples because slope has great importance in physical experimentation of Physics and Mathematics This quantity also has deep roots in different Mathematical fields or engineering.

**Table of Contents**

## How to Calculate the Slope of a line?

To calculate the slope, you only have to find a **change in position along the y-axis** (height) and a **change in position along the x-axis** (horizontal distance).

Here is the formula to find the change in vertical and horizontal positions.

Change in x = x_{2}- x_{1}(Horizontal Distance)

Change in y = y_{2}- y_{1}(Vertical Distance)

Here is the formula to find the slope:

Slope = Change in y / Change in x

**Note:**

The slope is also called the **Gradient** which you can read in detail here.

### Examples to Find Slope

**Example 1**

What is the slope of a line if a change in vertical distance is 8 and a change in horizontal distance is 3?

**Solution**:

As we know,

Slope = Change in y / Change in x

Slope = 8 / 3

Slope = 2.66

**Example 2:**

Find the Slope of a line while the change in x is 7 and the change in y is 63.

**Solution**:

We know that,

Slope = Change in y / Change in x

Slope = 63 / 7

Slope = 9

### Particular Notes about Slope

The slope is one of those quantities of Mathematics that can have both positive and negative values. It depends on the direction of quantities in terms of which we are calculating slope.

- The value of slope will be positive when a body or point is moving from left to right or down to top.
- The value of slope will be negative when a body o point is moving from right to left or top to down.

### Special Lines & their Slopes

The slope of a horizontally straight line is “0”. Why? It is because the change in y will be zero in such a line that will give “0” as the result of the formula.

The slope of a vertically straight line is “**Undefined**”. Why? It is because the **change in x will be zero** which means the denominator is “0”. Then, the resultant will be “**Undefined**” and you will not be able to find “**Something divided by 0**”.

### Special Note Regarding Slope

- The slope of a line has no units because it is the ratio between two same quantities (lengths).
- The slope of a line can also find using the trigonometric ratio “Tan” because it is also a ratio between height and horizontal distance.

### FAQ's

**What is the slope of a vertical line? **

The Slope of a vertical line is always undefined because the change in the horizontal direction will be zero which makes the answer undefined.

**What is the slope of a horizontal line?**

A horizontal line will have a 0 slope value because there will be no change in the y direction.

**Why slope of a vertical line is undefined?**

The vertical line will give an undefined slope because the denominator of the equation becomes zero as there is no change in the horizontal direction.