## Linear Functions

- Linear means
**straight** - A
**linear function**is a**straight line** - A
**linear graph**represents a**linear function**

## Linear Functions

A **Function **is special relationship where each input has an output.

A function is often written as **f(x)** where x is the input:

Results from f(x) = x

x | y | y = x |
---|---|---|

1 | 1 | y = x = 1 |

2 | 2 | y = x = 2 |

3 | 3 | y = x = 3 |

4 | 4 | y = x = 4 |

5 | 5 | y = x = 5 |

Results from f(x) = 2x

x | y | y = 2x |
---|---|---|

1 | 2 | y = 2x = 2 |

2 | 4 | y = 2x = 4 |

3 | 6 | y = 2x = 6 |

4 | 8 | y = 2x = 8 |

5 | 10 | y = 2x = 10 |

## Linear Equations

A Linear Equation is an equation for a straight line:

- y = x
- y = x*2
- y = x*2 + 7
- y = ax + b
- 5x = 3y
- y/2 = 6

## Non-Linear Equations

A Linear Equation can NOT contain exponents or square roots:

- y = x**2
- y = Math.sqrt(x)
- y = Math.sin(x)

## Linear Regression

A Linear regression tries to model the relationship between two variables by fitting a linear graph to data.

One variable (x) is considered to be data, and the other (y) is considered to be dependent.

For example, a Linear Regression can be a model to relate the price of houses to their size.

## Linear Least Squares

Linear algebra is used to solve Linear Equations.

Linear Least Squares (LLS) is a set of formulations for solving statistical problems involved in Linear Regression.