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Proportional Relationships: Identifying and Analyzing Trends

Learn how to determine proportional relationships in quantities through constant ratios. Explore examples and analyze graphs to differentiate between proportional and non-proportional relationships effectively.

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Proportional Relationships: Identifying and Analyzing Trends

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  1. Section 1.4Proportional and nonproportional relationships EQ: How do I determine a proportional relationship?

  2. Notes: Identify 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

  3. Vocabulary • 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.

  4. Proportional vs. Non-Proportional • If two quantities are proportional, then they have a constant ratio. • If the ratio is not constant, the two quantities are said to be non-proportional.

  5. 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.

  6. Example (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 18 36 or 18 54 or 18 72 or 18 • 1 2 3 4 • 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.

  7. Example • 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.

  8. Example • 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.

  9. Example • 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.

  10. Essential question • Explain what makes two quantities proportional. • ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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