Constant of Proportionality
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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 = 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 =πd where π 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. yB. 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.
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