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 : \(r=dfrac{1}{3}\).