### Introduction

Probably the most important function and graph that you will use are those associated with the straight line. A large number of relationships between engineering variables can be described using a straight line or
**
linear
**
graph. Even when this is not strictly the case it is often possible to approximate a relationship by a straight line. In this Section we study the equation of a straight line, its properties and graph.

#### Prerequisites

- understand what is meant by a function
- be able to graph simple functions

#### Learning Outcomes

- recognise the equation of a straight line
- explain the significance of $a$ and $b$ in the equation of a line $f\left(x\right)=ax+b$
- find the gradient of a straight line given two points on the line
- find the equation of a straight line through two points
- find the distance between two points

#### Contents

1 Linear functions2 The gradient of a straight line through two points

3 The equation of a straight line through two points

4 The distance between two points