CONSTANT OF PROPORTIONALITY

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 = 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. 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.

Quick Summary

The constant of proportionality (k) relates two directly proportional quantities.
k = x/y, where x and y are the two quantities.
The constant of proportionality can never be zero.

\[ x = ky; k = x/y \]

🍎 Teacher Insights

Use real-world examples, such as the relationship between distance and time at a constant speed, to illustrate the concept of constant proportionality. Emphasize the distinction between direct and inverse proportionality.

🎓 Prerequisites

Ratio
Proportion
Direct Variation

Check Your Knowledge

Q1: Ethan pays $30 per day for his stay in a hotel. What is the constant of proportionality that relates his rental charges (y) to the number of days (x) he stays in the hotel?

y x 30 x and y

Q2: If y = 5x, what is the constant of proportionality?

y x 5 0

Frequently Asked Questions

Q: What happens if the constant of proportionality is zero?
A: If the constant of proportionality is zero, then one of the quantities is always zero, regardless of the other quantity's value. This means there is no proportional relationship.

Q: How do I find the constant of proportionality?
A: Divide the dependent variable (x) by the independent variable (y). The result is the constant of proportionality (k = x/y).