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