Representing Proportional Relationships

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Presentation transcript:

Representing Proportional Relationships 3.1 Representing Proportional Relationships How can you use tables, graphs, and equations to represent proportional situations?

Texas Essential Knowledge and Skills The student is expected to: Proportionality—8.5.A Represent linear proportional situations with tables, graphs, and equations in the form of y = kx. Mathematical Processes 8.1.D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

ADDITIONAL EXAMPLE 1 Marco earns $36.50 per hour as an accountant. Show that the relationship between the amount he earns and the number of hours he works is a proportional relationship. Then write an equation for the relationship. y = 36.5x, where x is the number of hours, and y is the amount earned.

ADDITIONAL EXAMPLE 2 The graph shows the relationship between the number of days a car is rented and the total cost for the rental. Write an equation for this relationship.

3.1 LESSON QUIZ 8.5.A 1. Nico earns $12.50 per hour as a math tutor. Show that the relationship between the amount he earns and the number of hours he tutors is a proportional relationship. Then write the equation for the relationship. y = 12.5x, where x is the number of hours and y is the amount earned.

2. The graph shows the relationship between the number of cups of flour and the number of cookies made. Write an equation for the proportional relationship. y = 16x

3. The table shows a proportional relationship. Write an equation that describes the relationship. y = 28x

The table and graph show values representing a proportional relationship. Use the graph labels to describe the proportional relationship. Complete the table and graph the points from the table. Then write an algebraic equation for the proportional relationship.

The number of calories burned by a 90-pound cyclist is proportional to the number of hours the cyclist rode. The constant of proportionality is 225, and an equation for the proportional relationship is y = 225x.

How can you use tables, graphs, and equations to represent proportional situations? Sample answer: If the ratio between one quantity and another is constant, you can use tables, graphs, and equations of the form y = kx to represent a proportional relationship between the quantities.