## The Lesson

A constant is a number with a fixed value - its value does not change.## Dictionary Definition

The Merriam-Webster dictionary defines a constant as "a number that is assumed not to change value in a given mathematical discussion."## Real Examples of Constants

In algebra, some values always stay the same. They are constants. Numbers are examples of constants - a number can only have one value. 2 can only have a value of 2.Sometimes we use letters to stand in for constants. These letters will still stand in for a number which will always be the same. For example, π (pi) always has a value of 3.14.

In algebra, numbers that are not constants are called variables - they can change in value.

## Understanding Constants

It is easier to understand constants with an example. Let's look at an algebraic equation. Consider a linear equation:The

**2**and the

**1**are both constants. They both have a fixed value. The

*x*and the

*y*are variables. We can change their value. The values of

*x*and

*y*must keep both sides of the equation the same. The left hand side (

*y*) must be the same as the right hand side (

**2**

*x*+

**1**).

*x* = 1 ∴ *y* = **2***x* + **1** = **2** × 1 + **1** = 3

*x* = 2 ∴ *y* = **2***x* + **1** = **2** × 2 + **1** = 5

*x* = 3 ∴ *y* = **2***x* + **1** = **2** × 3 + **1** = 7

*x*and

*y*are allowed by the equation. Different constants would mean different pairs of

*x*and

*y*would be allowed by the equation.

## Coefficients Are a Type of Constant

A constant in front of a variable is called a coefficient. For example, consider the equation shown below:**2**and 1 are both constants in this equation. The

**2**is in front of the

*x*.

**2**is the coefficient of

*x*. It means

**2**×

*x*.