# Proportional relationship

**Proportional relationships** are "the more the more"-relationships.

They always **increase evenly** (proportionally) .

### Example

A bread costs 2 euros. The price of each additional bread **increases** equally.

Breads | Price (in €) |
---|---|

1 | 2 |

2 | 4 |

3 | 6 |

4 | 8 |

The graph is a **straight line** and always goes through the origin $O(0|0)$.

!

### Remember

Doubling (tripling, quadrupling, ...) an initial value, doubles (triples, quadruples, ...) also the assigned value.

## Constant of proportionality

If we divide the assigned size by the output size in a proportional relationship, we always get the same value.

### Example

Breads | Price (in €) |
---|---|

1 | 2 |

2 | 4 |

3 | 6 |

4 | 8 |

$2:1=\color{blue}{2}$

$4:2=\color{blue}{2}$

$6:3=\color{blue}{2}$

$8:4=\color{blue}{2}$

Here the constant of proportionality is 2. It is therefore a proportional relationship.

!

### Remember

The

**constant of proportionality**is the quotient of the assigned value (y) and the initial value (x).With the constant of proportionality $q$ you can immediately calculate the assigned value:

$y=x\cdot q$

$\text{assigned value}$ $=\text{initial value}$ $\cdot\text {constant of proportionality}$

### Example

Breads | Price (in €) |
---|---|

$1$ | $2= \color{blue}{2}\cdot1$ |

$2$ | $4 = \color{blue}{2}\cdot2$ |

$3$ | $6 = \color{blue}{2}\cdot3$ |

$4$ | $8 = \color{blue}{2}\cdot4$ |