Math Relationships Relationship ratio

# Relationship ratio

Relationships can sometimes be described exactly by a mathematical ratio.

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### Remember

A relationship ratio allows the calculation of the assigned value $y$ from the initial variable $x$.

The relationship ratios of proportional and inversely proportional relationships look different.

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## Proportional relationship

For proportional relationships, the relationship ratio is:

$y=q\cdot x$

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

### Example

12
24
36
......

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

The constant of proportionality is 2. The relationship ratio is:

$y=2x$

## Inversely proportional relationship

For Inversely proportional relationships the relationship ratio is:

$y=q\cdot \frac1x$

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

### Example

Workerneeded days
112
26
34
......

$1\cdot12=\color{blue}{12}$
$2\cdot6=\color{blue}{12}$
$3\cdot4=\color{blue}{12}$

The constant of inverse proportionality is 12. The relationship ratio is:

$y=\frac{12}x$