S ECTION 1.4 P ROPORTIONAL AND NONPROPORTIONAL RELATIONSHIPS EQ: How do I determine a proportional relationship?

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S ECTION 1.4 P ROPORTIONAL AND NONPROPORTIONAL RELATIONSHIPS EQ: How do I determine a proportional relationship?

N OTES : I DENTIFY PROPORTIONAL RELATIONSHIPS Two quantities are ____________ if they have a constant ratio or unit rate. For relationships in which this ratio is not constant, the two quantities are _______________. Cost of order = 8 = 16 = 24 = 32 = 40 Pizzas ordered = 1 = 2 = 3 = 4 = 5 or $8 per pizza

V OCABULARY Proportional: For a relationship to be constant there has to be a constant ratio. The graph of a proportional relationship will cross through the origin (0,0) Nonproportional: No constant ratio. The graph will not cross the origin.

P ROPORTIONAL VS. N ON -P ROPORTIONAL If two quantities are proportional, then they have a constant ratio. If the ratio is not constant, the two quantities are said to be nonproportional.

EXAMPLE 1. Andrew earns $18 per hour for mowing lawns. Is this amount of money he earns proportional to the number of hours he spends mowing? Explain. Find the amount of money he earns for working a different number of hours. Make a table to show these amounts. Earnings ($) Time (h)1234

E XAMPLE ( CONTINUED ) For each number of hours worked, write the relationship of the amount he earned and hour as a ratio in simplest form. 18 or or or or All of the ratios between the quantities can be simplified to 18. The amount of money he earns is proportional to the number of hours he spends mowing.

E XAMPLE 2. At Lakeview Middle School, there are 2 homeroom teachers assigned to ever 48 students. Is the number of students at this school proportional to the number of teachers? Explain your reasoning. Homeroom Teachers (h) Students (s)

E XAMPLE 3. At the beginning of the year, Isabel had $120 in the bank. Each week, she deposits another $20. Is her account balance proportional to the number of weeks of deposits? Use the table below. Explain your reasoning. Beginning of the year (y) Deposits (d)

E XAMPLE The Vista Marina rents boats for $25 per hour. In addition to the rental fee, there is a $12 charge for fuel. Is the number of hours you can rent the boat proportional to the total cost? Explain. Rental Time (h) Cost ($)

E SSENTIAL QUESTION Explain what makes two quantities proportional. ______________________________________________ ______________________________________________ ______________________________________________ ______________________________________________ ______________________________________________