Mathematics
Grade 7
15 min
Find the constant of proportionality: word problems
Find the constant of proportionality: word problems
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1
Introduction & Learning Objectives
Learning Objectives
Identify proportional relationships within word problems.
Define the constant of proportionality and explain its role.
Correctly identify the independent (x) and dependent (y) variables in a given word problem.
Calculate the constant of proportionality (k) from numerical information presented in word problems.
Interpret the meaning of the constant of proportionality in the context of a real-world problem.
Write an equation in the form y = kx to represent a proportional relationship described in a word problem.
Ever wonder how much you earn per hour, or how many miles your car travels per gallon? ⛽️ These are all examples of proportional relationships!
In this lesson, you'll learn to identify and calculate the 'constant of proportionality'...
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Key Concepts & Vocabulary
TermDefinitionExample
Proportional RelationshipA relationship between two quantities where one is a constant multiple of the other. This means their ratio is always the same, and when graphed, it forms a straight line passing through the origin (0,0).If you earn $12 for every 2 hours you work, you earn $24 for 4 hours, and $36 for 6 hours. The ratio of money to hours is always $6 per hour.
Constant of Proportionality (k)The constant ratio between two proportional quantities, often represented by the letter 'k'. It is the unit rate of the relationship.In the relationship where you earn $6 per hour, the constant of proportionality (k) is 6. This means for every 1 unit of the independent variable, the dependent variable changes by 6 units.
Unit RateA rate where the second quantity...
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Core Formulas
Formula for Constant of Proportionality
$k = \frac{y}{x}$
To find the constant of proportionality (k), divide the dependent variable (y) by the independent variable (x). This formula works for any point (x, y) in a proportional relationship, except for the origin (0,0).
Equation of a Proportional Relationship
$y = kx$
Once you have found the constant of proportionality (k), you can write an equation that describes the entire proportional relationship. This equation allows you to find 'y' for any given 'x', or vice versa.
5 more steps in this tutorial
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Challenging
A machine's operating time is described by the equation H = (1/40)W, where H is the time in hours and W is the number of widgets produced. What is the constant of proportionality, k, that represents the production rate in 'widgets per hour'?
A.1/40
B.40
C.20
D.0.025
Challenging
The perimeter of any regular pentagon (5 equal sides) is proportional to its side length. What is the constant of proportionality that relates the perimeter (y) to the side length (x)?
A.2.5
B.4
C.5
D.It depends on the side length.
Challenging
A store offers a proportional discount. A customer who spends $150 receives a discount of $22.50. Another customer buys an item that was originally $240. What is the final price this customer pays after the discount?
A.$36.00
B.$204.00
C.$217.50
D.$225.00
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