Proportional Relationships
3.1 Lesson
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Mrs. Carley
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Definitions
• Proportional Relationship - it is a relationship
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between two quantities in which the ratio of
one quantity to the other quantity is constant.
– Example: The amount a person earns and the
number of hours a person works.
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• Constant of proportionality: an equation written
as k = y/x
Representing Proportional Relationships with Equations:
Example #1
• Megan earns $12 an hour at her part-time
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job. Show that the relationship between the
amount she earned and the number of hours
she worked is a proportional relationship.
Then write an equation for the relationship.
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– Step 1: Make a table to relating amount earned
to number of hours.
Number of
hours
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Amount
Earned ($)
$12.00
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Example #1 Continued:
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• Step #2: For each number of hours, write a
relationship of the amount earned and the
number of hours as a ratio in simplest form.
• Step #3: Write an equation.
– Let x represent:
– Let y represent:
– The equation is
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Another Example
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• Marco earns $36.50 per hour as an
accountant. Show that relationship between
the amount he earns and the number of
hours he works is a proportional
relationship. Then write an equation for the
relationship.
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Example Answer:
Step #1: Make a table
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# of Hours
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4
Amount
Earned
$36.50
$73.00
(36.50 * 2)
$109.50
(36.50 *3)
$146.00
(36.50 *4)
Step #2: Write a proportional relationship:
Amount earned
Number of hours worked
$36.50
1
$73.00
2
$109.50
3
$146.00
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Step #3: Write an equation for the relationship
x = number of hours
y = amount of hours worked
$36.50/1 = 36.50 $73/2 = 36.50 $109.50/3 = 36.50
Equation: y = 36.50x
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$146/4 = 36.50
Representing Proportional Relationships with Graphs:
Example #2
• Look at page 73 in your textbook at Example #2
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– Step 1: Use the points on the table to make a graph.
– Step 2: Find the constant of proportionality.
• Moon weight 1
Earth weight 6
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– Step 3: Write an equation
• X = weight on earth
• Y = 1/6x
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Y = weight on moon
• Complete “Your Turn” on page 73