**Definition of Constant of Proportionality**

- If a quantity
*x*is proportional (directly) to another quantity*y*, then*x*is written as*x = ky*, where*k*is called the Constant of Proportionality.

**More about Constant of Proportionality**

- The constant ratio between two quantities is also called as constant of proportionality i.e. if
*x*is proportional (directly) to*y*, then*k*= . - The constant of proportionality can never be zero.

**Example of Constant of Proportionality**

- Circumference (
*C*) of a circle is proportional to its diameter (*d*). Circumference of a circle is given as*C*=*πd*where*π*is the constant of proportionality.

**Solved Example on Constant of Proportionality**

Ethan pays $30 per day for his stay in a hotel. Identify the constant of proportionality that relates his rental charges (

y) to the number of days (x) he stays in the hotel.

Choices:

A.y

B.x

C. 30

D.xandy

Correct Answer: C

Solution:

Step 1:As the rental charges and the number of days vary directly, the equation is of the formy=kx, wherekis the constant of proportionality.

Step 2:y= (30)x[Substitutek= 30.]

Step 3:y= 30xis the direct variation model that relates the rental charges to the number of days.

Step 4:Therefore, 30 is the constant of proportionality.

**Related Terms for Constant of Proportionality**

- Constant
- Proportional Relationships
- Quantity
- Ratio