Math Relationships Proportional relationship

# Proportional relationship

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

They always increase evenly (proportionally) .

### Example

12
24
36
48

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

12
24
36
48

$2:1=\color{blue}{2}$
$4:2=\color{blue}{2}$
$6:3=\color{blue}{2}$
$8:4=\color{blue}{2}$

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

$1$$2= \color{blue}{2}\cdot1 2$$4 = \color{blue}{2}\cdot2$
$3$$6 = \color{blue}{2}\cdot3 4$$8 = \color{blue}{2}\cdot4$