Objectives

1. 1.5 Representing Linear Patterns Objectives • Represent linear patterns with equations. • Represent linear equations with graphs.

2. 1.5 Representing Linear Patterns Glossary Terms dependent variable independent variable linear equation

3. 15 15 15 15 15 1.5 Representing Linear Patterns Write and graph linear equations representing problem situations. A DVD buyers club charges $20 membership fee and $15 per DVD purchased. 1st differences The equation c = 15d + 20 represents the situation, where c represents the total cost, and d represents the number of DVDs.

4. 1.5 Representing Linear Patterns Is it possible to graph this situation from the data in the table, if so, what values represent the x and y for the ordered pairs? DVD = x-coordinate and ($) = y-coordinate List the ordered pairs: (0, 20) (2, 50) (4, 80) (1, 35) (5, 95) (3, 65)

5. (0, 20) (2, 50) (4, 80) DVD Membership (1, 35) (3, 65) (5, 95) 0 1 2 3 4 5

6. 13 13 13 13 13 1.5 Representing Linear Patterns Ex 1: Find the differences, write an equation and graph the data. The cost associated with being a member of a DVD buyers club are represented in the table below. 1st differences The equation c = 13d + 26 represents the situation, where c represents the total cost, and d represents the number of DVDs.

7. 1.5 Representing Linear Patterns Is it possible to graph this situation from the data in the table, if so, what values represent the x and y for the ordered pairs? DVD = x-coordinate and ($) = y-coordinate List the ordered pairs: (0, 26) (2, 52) (4, 78) (1, 39) (5, 91) (3, 65)

8. (0, 26) (2, 52) (4, 78) DVD Membership (1, 39) (3, 65) (5, 91) 0 1 2 3 4 5

9. 1.5 Representing Linear Patterns Ex 1: The table show the cost associated with an Audio CD club that charges membership fee. Write an equation to represent the pattern from the data. c = 10d + 21

10. 1.5 Representing Linear Patterns Ex 1a: The table show the cost associated with a CD club that charges membership fee. Write an equation to represent the pattern from the data. c = 9d + 25

11. 1.5 Representing Linear Patterns Ex 1b: A passenger ferry from Seattle, Washington, to Victoria, British Columbia, travel at a rate of 53 miles per hour. The distance the ferry travels in a given period of time can be represented by the following: distance = rate • time 132.5 79.5 106 Complete the table of values for d = 53t How far will the ferry travel in 4 hours? 212 mi

12. 1.5 Representing Linear Patterns Ex 2: A jet airplane is flying at a rate of 280 miles per hour. Write a linear equation to express the distance traveled in a given amount of time. Graph the results from 0 to 10 hours. distance = rate • time d = 280t t = 0, 2, 5, 10 hours 1400 2800 560

13. Jet Liner 0 1 2 3 4 5 6 7 8 9 10

14. 1.5 Representing Linear Patterns Ex 2a: Jeremy drives at an average rate of 50 mph. Write a linear equation to express the distance traveled in a given amount of time. Graph the results from 0 to 10 hours. distance = rate • time d = 50t t = 0, 2, 5, 10 hours 300 500 100

15. Jeremy’s Driving 0 1 2 3 4 5 6 7 8 9 10

16. 1.5 Representing Linear Patterns Ex 3: Exercise physiologists suggest that a reasonable estimate for the maximum heart rate during exercise is no more than 220 beats per minute minus the person’s age. Represent the maximum heart rate by r, and the age by a. Write a linear equation to express the maximum heart rate, hr, in terms of age, a. Graph the results for ages 10 to 50. hr = 220 - a 210 170 190 200 180

17. Heart Rate 0 20 40 60 80