How to Find the Constant of Proportionality?
Below are the steps to Find the Constant of Proportionality.
- To find the constant of proportionality: you can conduct experiments, gather data points and use the formula ‘k = y / x.’
- Alternatively, you can analyse the data graphically and determine ‘k’ from the slope of the line on a graph representing the proportional relationship.
Example: Suppose the cost of buying 4 books is Rs. 600 and cost of buying two books is Rs. 300. Find the constant of proportionality for the cost of buying books.
Solution:
In this example, we have a direct proportion between the number of books (x) and the cost (y).
To find the constant of proportionality, you can use the formula for direct proportion, which is:
y = kx
Where,
- y is the cost of the books,
- x is the number of books, and
- k is the constant of proportionality that we want to find.
Given that when you buy 4 books, the cost is $60, you can plug these values into the formula:
600 = k × 4 OR 300 = k × 2
Now, solve for k:
k = 600 / 4 OR k = 300/2
Thus, k = 150
Constant of Proportionality
Constant of Proportionality is a fundamental concept in mathematics that helps us understand the relationships between two varying quantities. Constant of Proportionality is used for analyzing direct and inverse relationships in various contexts. Constant of Proportionality represents the unchanging value in the ratio between two directly or inversely proportional quantities.
Constant of Proportionality is often denoted as ‘k’ that relates two directly or inversely proportional quantities. In this article, we will discuss the Constant of Proportionality in detail including its definition and types. We will also have a look at various solved examples on the Constant of Proportionality concept for understanding.
Table of Content
- What is Proportionality?
- What is Constant of Proportionality?
- Constant of Proportionality Formula
- Direct and Inverse Proportions
- How to Find the Constant of Proportionality?
- Use of Constant of Proportionality
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