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

  • 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. 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.

Related Terms for Constant of Proportionality

  • Constant
  • Proportional Relationships
  • Quantity
  • Ratio