Constant of Proportionality

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

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

Video Examples: The Constant of Proportionality


Example of Constant of Proportionality

    Circumference (C) of a circle is proportional to its diameter (d). Circumference of a circle is given as
    C = pd where p is the constant of proportionality.

Solved Example on Constant of Proportionality

Ques: 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. x and y
    Correct Answer: C

Solution:

    Step 1: As the rental charges and the number of days vary directly, the equation is of the form y = kx, where k is the constant of proportionality.
    Step 2: y = (30)x [Substitute k = 30.]
    Step 3: y = 30x is the direct variation model that relates the rental charges to the number of days.
    Step 4: Therefore, 30 is the constant of proportionality.