Proportional Relationships and Graphs

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Presentation transcript:

Proportional Relationships and Graphs 2.3 Proportional Relationships and Graphs How can you use graphs to represent and analyze proportional relationships?

Texas Essential Knowledge and Skills The student is expected to: Proportionality—7.4.A Represent constant rates of change in mathematical and real-world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt. Proportionality—7.4.C Determine the constant of proportionality within mathematical and real-world problems. Proportionality—7.4.D Solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems.

Texas Essential Knowledge and Skills The student is expected to: Mathematical Processes 7.1.D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

ADDITIONAL EXAMPLE 1 A test car went 64 miles on 2 gallons in the morning, 16 miles on gallon at noon, and 32 miles on 1 gallon at 5 pm. Is the relationship a proportional relationship? The graph of the data is a line that goes through the origin. So, the relationship is proportional.

ADDITIONAL EXAMPLE 2 The graph shows the relationship between the number of concert tickets purchased and the total cost for the tickets. Write an equation for this relationship. y = 20x

2.3 LESSON QUIZ 7.4.A The following data was collected on a cheetah. It ran mile in min, mile in min, and mile in 1 min. 1. Explain how you know that this is a proportional relationship. The ratio of each data set simplifies to 0.75. 2. Identify the constant of proportionality, and write an equation for the proportional relationship. 0.75; y = 0.75x

The following data was collected on a cheetah The following data was collected on a cheetah. It ran mile in min, mile in min, and mile in 1 min. 3. Make a table and a graph of the proportional relationship.

The following data was collected on a cheetah The following data was collected on a cheetah. It ran mile in min, mile in min, and mile in 1 min. 4. Identify a point on the graph that gives the constant of proportionality as the y-coordinate. (1, 0.75)

The graph shows one point on the graph of a proportional relationship The graph shows one point on the graph of a proportional relationship. Use the graph labels and what you have learned about proportional relationships to describe a possible proportional relationship that it represents, and identify the constant of proportionality. Then write an algebraic equation for the proportional relationship.

The point (5, 1) is graphed. This represents 1 mile in 5 minutes, or a unit rate of mile per minute. The constant of proportionality is and an equation for the proportional relationship is y = x.

How can you use graphs to represent and analyze proportional relationships? Sample answer: A graph that is a line through the origin shows a proportional relationship.