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**Proportional Relationships**

Quantities have a constant ratio, or unit rate Nonproportional relationships: Quantities do not have a constant ratio, or unit rate

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Example 1: The following chart shows how much money Layla earns babysitting. Is the amount of money she earns proportional to the number of hours that she spends babysitting? Hours (h) Money earned ($) 1 5.50 2 11.00 3 16.50 4 22.00 Find the unit rate of money earned to hours worked for each pair of values. There is a proportional relationship between money earned and hours since all of the ratios have a unit rate of

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**Plot points (x, y) from the table.**

Let’s graph this proportional relationship from Ex. 1 on an xy-plane. We typically put time (hours) on the x-axis, and the money earned ($) on the y-axis. y Layla’s Babysitting Money Plot points (x, y) from the table. 22.00 Hours (h) Money Earned ($) Point (x, y) 1 5.50 (1, 5.50) 2 11.00 (2, 11) 3 16.50 (3, 16.50) 4 22.00 (4, 22) 16.50 Money Earned ($) 11.00 5.50 x 1 2 3 4 5 Hours worked The graph of a proportional relationship: is a straight line, AND it passes through the origin, or point (0,0).

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**In words, Money earned = (money per hour)(number of hours)**

We can write an equation to represent the proportional relationship from Ex. 1. x y Hours worked Money Earned ($) 1 5.50 11.00 16.50 22.00 2 3 4 5 Layla’s Babysitting Money Hours (h) Money Earned ($) 1 5.50 2 11.00 3 16.50 4 22.00 In words, Money earned = (money per hour)(number of hours) As an equation, y = $5.50 x

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Example 2: Movie World charges a $6 monthly membership fee plus $1 per movie rental. Is the monthly cost proportional to the number of movies rented? Explain . Find the unit rate of the monthly cost to the number of rentals for each pair of values. Movies rented 1 2 3 4 Monthly Cost ($) 7 8 9 10 There is NOT a proportional relationship between monthly cost and number of movie rentals since all of the ratios between the two quantities are not equal.

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**Let’s look at a graph this nonproportional relationship from Ex. 2.**

Movie rentals will be on the x-axis, and the monthly cost ($) will be on the y-axis. Monthly Cost of Movies from Movie World y 16 Rentals Monthlycost ($) Point (x, y) 1 7 (1, 7) 2 8 (2, 8) 3 9 (3, 9) 4 10 (4, 10) 14 12 10 Cost ($) 8 6 4 2 This graph shows a nonproportional relationship. Even though this graph is a straight line, it does not pass through the origin. x 1 2 3 4 Number of movie rentals

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A constant ratio in any proportional relationship Really just another name for unit rate! Remember, to be constant means it never changes!

A constant ratio in any proportional relationship Really just another name for unit rate! Remember, to be constant means it never changes!

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