# Gradient of a straight line

## Prerequisites

### Gradient of a straight line

#### Introduction

• A gradient describes how much y changes relative to a change in x.
• For example, we can define a line as starting at (0, 0) and ending at (10, 25):
• Instead of giving explicit start and end points for the line we can describe it by how much y changes relative to x.
• In the line above, a change of 10 in x produces a change of 25 in y.
• The gradient is defined as the change in y divided by the change in x.
• If we use Δ to denote 'change' then the formula for the gradient (g) of a line is:
LaTeX formula:g = \frac{\Delta y}{\Delta x}
• In the line above, the gradient is:

#### Finding the change in x and y

• In our above example, our first coordinate was (0, 0). This made it easy to calculate how much x and y changed.
• However when both coordinates are non-zero, it gets a bit more complicated.
• For example, calculate the gradient of the line between (1, 2) and (7, 10)
1. To find how much x and y change, we need to subtract the first coordinate from the second
• We can use this in our equation to find the gradient of any line:

#### Special Cases

• There are two special cases to look out for when calculating the gradient of a line:
1. When the line is horizontal
• There will be no change in y
2. When the line is vertical
• There will be no change in x

import math