Mathematics
Grade 8
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.
Define the constant of proportionality (k) and its significance.
Select appropriate points from a graph to calculate the constant of proportionality.
Accurately calculate the constant of proportionality (k) using the formula k = y/x.
Interpret the meaning of the constant of proportionality in real-world contexts.
Write the equation of a proportional relationship (y = kx) from its graph.
Have you ever noticed how the cost of buying multiple identical items often follows a predictable pattern? 🍎💰 What if we could see that pattern on a graph and easily figure out the price per item?
In this lesson, you'll learn how to analyze graphs to determine if a relationship is proportional and, if so, h...
2
Key Concepts & Vocabulary
TermDefinitionExample
Proportional RelationshipA relationship between two quantities where their ratio is constant. On a graph, it is represented by a straight line that passes through the origin (0,0).The relationship between the number of hours worked and the money earned, if the hourly wage is constant. If you work 2 hours and earn $20, and 4 hours and earn $40, it's proportional.
Constant of Proportionality (k)The constant ratio between two proportional quantities, typically represented as y/x. It represents the unit rate of the relationship.If a car travels 120 miles in 2 hours, the constant of proportionality is k = 120/2 = 60 miles per hour.
OriginThe point (0,0) on a coordinate plane where the x-axis and y-axis intersect. All proportional relationships must pass through this...
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Core Formulas
Identifying a Proportional Graph
A graph represents a proportional relationship if and only if it is a straight line that passes through the origin (0,0).
Before calculating the constant of proportionality, always check these two conditions. If either is not met, the relationship is not proportional.
Formula for Constant of Proportionality
$k = \frac{y}{x}$
To find the constant of proportionality (k) from any point (x, y) on a proportional graph (excluding the origin), divide the y-coordinate by the x-coordinate.
Equation of a Proportional Relationship
$y = kx$
Once you find the constant of proportionality (k), you can write an equation that describes the entire relationship. This equation allows you to find any y-value for a given x-value.
5 more steps in this tutorial
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Challenging
The graph of a proportional relationship passes through the point (c, 5c) where c is not zero. What is the constant of proportionality?
A.c
B.5c
C.5
D.1/5
Challenging
A graph shows the cost of two types of cheese. Line F (feta) passes through (2 lbs, $10). Line C (cheddar) passes through (3 lbs, $18). Both are proportional relationships. Which statement is true?
A.The cheddar is more expensive per pound because its line is steeper.
B.The feta is more expensive per pound because its line is steeper.
C.They cost the same per pound.
D.The cheddar is more expensive per pound because its line is less steep.
Challenging
A graph shows distance (y, in meters) vs. time (x, in minutes). The x-axis scale is 1 grid line = 2 minutes. The y-axis scale is 1 grid line = 150 meters. A point on the proportional graph is at (4 grid lines right, 3 grid lines up). What is the speed in meters per minute?
A.50
B.75
C.112.5
D.56.25
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