# Relationship of Proportionality

## Relationship of Proportionality

Relationship between real numbers, such that, for all real numbers x and y, there exists a real number r such that $$\dfrac{x}{y}=r$$.

The number r is called the ratio of proportionality or the proportionality constant.

### Examples

A relationship of proportionality defines a linear function of the form f(x) = mx, where the parameter m (called the slope of the graph of f) is the coefficient of proportionality.

Consider the following sequences 1 and 2 :

Sequence 1 :    2     5     8     11     14     17     20
Sequence 2 :    6    15    24   33     42     51     60

Each term in sequence 1 is multiplied by 3 to obtain each term in sequence 2.
Therefore, the relationship of proportionality between the sequences 1 and 2 is : $$r=dfrac{1}{3}$$.