Mathematics
Grade 7
15 min
Find the constant of proportionality from a graph
Find the constant of proportionality from a graph
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1
Introduction & Learning Objectives
Learning Objectives
Identify graphs that represent proportional relationships.
Accurately read ordered pairs (x, y) from a graph.
Calculate the constant of proportionality (k) using the ratio y/x from a graph.
Interpret the meaning of the constant of proportionality in the context of a given problem.
Verify the constant of proportionality using multiple points on a graph.
Write the equation y = kx for a proportional relationship shown on a graph.
Ever wonder how much juice concentrate you need for a big party, or how many miles you can drive on a certain amount of gas? ⛽️ Graphs can help us find a special number that tells us how things are related!
In this lesson, you'll learn how to find this special number, called the 'constant of proportionality,' direct...
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Key Concepts & Vocabulary
TermDefinitionExample
Proportional RelationshipA relationship between two quantities where their ratio is constant. When one quantity changes, the other changes by a consistent factor.If 2 apples cost $1, then 4 apples cost $2. The ratio of cost to apples is always $0.50 per apple.
Constant of Proportionality (k)The constant ratio y/x in a proportional relationship. It represents the unit rate or the amount of 'y' for every one unit of 'x'.In the apple example, k = $1 / 2 apples = $0.50 per apple.
Graph of a Proportional RelationshipA straight line that passes through the origin (0,0) on a coordinate plane.A graph showing distance traveled vs. time for a car moving at a constant speed will be a straight line starting from (0,0).
OriginThe point (0,0) on a coordinate pl...
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Core Formulas
Equation of a Proportional Relationship
$$y = kx$$
This equation describes any proportional relationship, where 'y' is the dependent variable, 'x' is the independent variable, and 'k' is the constant of proportionality.
Calculating the Constant of Proportionality
$$k = \frac{y}{x}$$
To find the constant of proportionality 'k', divide the 'y'-coordinate of any point on the graph (except the origin) by its corresponding 'x'-coordinate.
Graphical Properties of Proportional Relationships
A graph represents a proportional relationship if and only if it is a straight line that passes through the origin $$(0,0)$$.
This rule helps you quickly identify if a relationship shown on a graph is proportional before attempt...
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Challenging
A graph of a proportional relationship passes through the origin and the point (8, 6). What is the constant of proportionality?
A.8/6
B.1.33
C.0.75
D.14
Challenging
A graph shows a proportional relationship between two quantities, x and y. The line passes through the origin and a point labeled (p, q), where p and q are positive numbers. Which expression represents the constant of proportionality?
A.p * q
B.p / q
C.p + q
D.q / p
Challenging
A graph shows the distance (y, in miles) vs. time (x, in hours) for a road trip. The line is proportional and passes through (2, 120). The constant of proportionality, k, represents the car's speed in miles per hour. What does the value 1/k represent?
A.The total time of the trip in hours.
B.The total distance of the trip in miles.
C.The amount of time in hours it takes to travel one mile.
D.The car's speed in miles per minute.
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