# Linear Function

The equation of a **linear function** is:

**y = mx + b**

Its **graph** is an **oblique straight line**, which is defined by two points of the function.

y = x + 4

x | 0 | −4 |
---|---|---|

y = x + 4 | 4 | 0 |

**m** is the slope of the straight line.

The slope is the inclination of the line with respect to the x-axis.

If **m > 0**, the **function** is **increasing** and the **angle** of the line with the positive x-axis is **acute**.

If **m < 0**, the **function** is **decreasing** and the **angle** between the line with the positive x-axis is **obtuse**.

Two parallel lines have the same slope.

**n** is the **y-intercept** and indicates the intersecting point of the line with the vertical axis.

If **b = 0**, the equation of a **linear function** is:

**y = mx**

Its graph is a straight line passing through the origin.

y = 2x

x | 0 | 1 | 2 | 3 | 4 |
---|---|---|---|---|---|

y = 2x | 0 | 2 | 4 | 6 | 8 |

### Identity Function

**y = x**

Its graph is the bisector of the first and third quadrant.

#### Examples

1 y = 2x - 1

x | y = 2x-1 |
---|---|

0 | -1 |

1 | 1 |

2y = -¾x - 1

x | y = -¾x-1 |
---|---|

0 | -1 |

4 | -4 |