Agenda Ticket in the Door Review of ticket in the Door

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Proportional Relationships

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12.19.2017 Agenda Ticket in the Door Review of ticket in the Door Unit 3 Post Test Review Wrap-up Solve 3y + 2 = 11 Solve 1 4 x - 2 = 3

Unit 3 Post Test Review

Rate of change Constant rate of change Proportional relationships Vocabulary Rate of change Constant rate of change Proportional relationships

Guiding Questions How do you determine if a rate of change is constant from a table? A graph? What do you know about the rate of change if a relationship is described to be linear? How could you determine if a relationship is proportional or not?

The rate of change of a function is a ratios that compares the difference between two output values to the difference between the corresponding input values. The rate of change between any two points in a linear relationship is the same or constant. A linear relationship has a constant rate of change.

Be careful to put the difference in y-values in the numerator and the differences in x-values in the denominator when you write a rate of change. Caution!

Identify Linear Relationships BABYSITTING The amount a babysitter charges is shown. Is the relationship between the number of hours and the amount charged linear? If so, find the constant rate of change. If not, explain your reasoning. Lesson 10 Ex1

Identify Linear Relationships Examine the change in the number of hours worked and in the amount earned. Lesson 10 Ex1

Find a Constant Rate of Change TRAVEL Find the constant rate of change for the hours traveled and miles traveled. Interpret its meaning. Choose any two points on the line and find the rate of change between them. Lesson 10 Ex2

Find a Constant Rate of Change The amount of miles changed from 60 to 120 between hours 2 and 4. Subtract to find the change in miles and the change in time. Express this rate as a unit rate. Answer: The rate of speed is 30 miles per hour. Lesson 10 Ex2

A. The rate of speed is 20 miles per hour. TRAVEL Find the constant rate of change for the hours traveled and miles traveled. Interpret its meaning. A. The rate of speed is 20 miles per hour. B. The rate of speed is 25 miles per hour. C. The rate of speed is 40 miles per hour. D. The rate of speed is 50 miles per hour. A B C D Lesson 10 CYP2

Lesson 9 Concept Summary 1

To determine if two quantities are proportional, compare the ratio b/a for several pairs of points to determine if there is a constant ratio.

Identify Proportional Relationships TAXIS Use the graph to determine if there is a proportional linear relationship between the miles driven and the charge for a ride. Explain your reasoning. Since the graph of the data forms a line, the relationship between the two scales is linear. This can also be seen in the table of values created using the points on the graph. Lesson 10 Ex3

Lesson 10 Ex3 Identify Proportional Relationships To determine if the two scales are proportional, express the relationship between the charges for several miles as a ratio. Answer: Since the ratios are not all the same, the total charge is not proportional to the number of miles driven.

MOVIES Use the graph to determine if there is a proportional linear relationship between the number of movies rented and the total cost. Explain your reasoning. A. The data lie in a straight line and the ratio of the number of movies rented to the total cost is always the same, so there is a proportional linear relationship. B. The data lie in a straight line but the ratio of the number of movies rented to the total cost is not always the same, so there is not a proportional linear relationship. A B Lesson 10 CYP3

Lesson 10 Concept Summary 1

Guiding Questions (you should be able to answer) How do you determine if a rate of change is constant from a table? A graph? What do you know about the rate of change if a relationship is described to be linear? How could you determine if a relationship is proportional or not?

Reference: http://classroom.kleinisd.net/users/0241/images/Constant%20Rate%20of%20Change%20PowerPoint.pptx