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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 ($) 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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We typically put time (hours) on the x-axis, and the money earned ($) on the y-axis. Lets graph this proportional relationship from Ex. 1 on an xy-plane. x y Hours worked Money Earned ($) Hours (h) Money Earned ($) Point (x, y) 15.50(1, 5.50) (2, 11) (3, 16.50) (4, 22) Plot points (x, y) from the table. The graph of a proportional relationship: is a straight line, AND it passes through the origin, or point (0,0). Laylas Babysitting Money

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We can write an equation to represent the proportional relationship from Ex. 1. Hours (h) Money Earned ($) In words, Money earned = (money per hour)(number of hours) As an equation, y = $5.50 x x y Hours worked Money Earned ($) Laylas Babysitting Money

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Example 2: Movie World charges a $6 monthly membership fee plus $1 per movie rental. Is the monthly cost proportional to the number of movies rented? Explain. Movies rented1234 Monthly Cost ($)78910 Find the unit rate of the monthly cost to the number of rentals for each pair of values. 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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Movie rentals will be on the x-axis, and the monthly cost ($) will be on the y-axis. x y Number of movie rentals Cost ($) Rentals Monthly cost ($) Point (x, y) 17(1, 7) 28(2, 8) 39(3, 9) 410(4, 10) Lets look at a graph this nonproportional relationship from Ex This graph shows a nonproportional relationship. Even though this graph is a straight line, it does not pass through the origin. Monthly Cost of Movies from Movie World

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