1. Comparing Multiple Representations 9-4 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. Comparing Multiple Representations 9-4 Warm Up 1. Find the slope of a line through points (3, 4) and (6, 2). 2. The slope of a line is 2 and the y-intercept is 10. What is the slope-intercept form of the line? y = 2x + 10 -2-2 3

3. Comparing Multiple Representations 9-4 Problem of the Day Chicken salad costs $5 per person and egg salad costs $4 per person. Write these two options as linear functions and compare them in terms of the context. Chicken sal f(x) = 5x and egg sal g(x) = 4x; f has a greater rate of change (cost per person).

4. Comparing Multiple Representations 9-4 Learn to compare linear functions represented in different ways.

5. Comparing Multiple Representations 9-4 Remember that slope is rise (change in y) divided by run (change in x) or ‘rise over run’. Helpful Hint

6. Comparing Multiple Representations 9-4 Find and compare the slopes for the linear functions f and g. f(x) = 10x – 5 Additional Example 1: Comparing Slopes Find the slope of f. Function f is written in slope-intercept form. f(x) = mx + b f(x) = 10x – 5 The slope of f is 10. x–2–101 g(x)g(x)051015

7. Comparing Multiple Representations 9-4 Additional Example 1: Continued Find the slope of g. The slope of g is 5. The slope f is greater than the slope of g. m = y2 – y1y2 – y1 x2 – x1x2 – x1 10 – 5 0 – (–1) = = 5

8. Comparing Multiple Representations 9-4 Find and compare the slopes for the linear functions f and g. f(x) = 8x + 4 Check It Out: Example 1 x–2–101 g(x)g(x)081624 Find the slope of f. Function f is written in slope-intercept form. f(x) = mx + b f(x) = 8x + 4 The slope of f is 8.

9. Comparing Multiple Representations 9-4 Continued: Check It Out Example 1 Find the slope of g. The slope of g is 8. The slope f is the same as the slope of g. m = y2 – y1y2 – y1 x2 – x1x2 – x1 16 – 8 0 – (–1) = = 8

10. Comparing Multiple Representations 9-4 Additional Example 2: Comparing Intercepts Find the y-intercept of f. When x = 0, f(x) = –6. The y-intercept of f is –6. Find the y-intercept of g. Find and compare the y-intercepts for the linear functions f and g. The graph of g crosses the y- axis at about –5. The y-intercept of g is greater than the y-intercept of f. x0123 f(x)f(x)-6-4-20

11. Comparing Multiple Representations 9-4 Check It Out: Example 2 Find the y-intercept of f. When x = 0, f(x) = 3. The y-intercept of f is 3. Find the y-intercept of g. The graph of g crosses the y- axis at about 3.5. The y-intercept of f is greater than the y-intercept of g. x–1012 f(x)f(x)0369

12. Comparing Multiple Representations 9-4 Rate of change is given by the slope and initial value is given by the y-intercept of a linear function. Remember!

13. Comparing Multiple Representations 9-4 Additional Example 3: Application Fred and Gene are hang gliding. Fred is 700 feet above the ground and descending at 15 ft/s. Gene is descending as shown in the table. Interpret the rates of change and initial values of the linear functions in terms of the situations they model. f(x) = –15x + 700 Fred’s descent. f(x) = mx + b f(x) = –15x +700 The rate of change is –15. The initial value is 700. Time (sec)0123 Height (ft)575565555545

14. Comparing Multiple Representations 9-4 Additional Example 3: Continued The rate of change is –10. Gene’s descent. The initial value is 575. Gene’s rate of descent (10 ft/sec) is 5 ft/s less than Fred’s. Fred is 125 feet higher than Gene when they start. m = y2 – y1y2 – y1 x2 – x1x2 – x1 = = –10 565 – 575 1 – 0

15. Comparing Multiple Representations 9-4 Check It Out: Example 3 Fred and Gene are hang gliding. Fred is 600 feet above the ground and descending at 10 ft/s. Gene is descending as shown in the table. Interpret the rates of change and initial values of the linear functions in terms of the situations they model. f(x) = –10x + 600 Time (sec) 0123 Height (ft) 480465450435

16. Comparing Multiple Representations 9-4 Continued: Check It Out Example 3 Fred’s descent. f(x) = mx + b f(x) = –10x +600 The rate of change is –10. The initial value is 600.

17. Comparing Multiple Representations 9-4 Continued: Check It Out Example 3 The rate of change is –15. Gene’s descent. The initial value is 480. Fred’s rate of descent (10 ft/sec) is 5 ft/s less than Gene’s. Fred is 120 feet higher than Gene when they start. m = y2 – y1y2 – y1 x2 – x1x2 – x1 = = –15 465 – 480 1 – 0

18. Comparing Multiple Representations 9-4 Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

19. Comparing Multiple Representations 9-4 Use the function and graph for Items 1–2. f(x) = -2x + 3 1. Find and compare the slopes for the linear functions f and g. 2. Find and compare the y-intercepts for the linear functions f and g. Lesson Quiz : Part I f: 3, g: 4; y-int. g > y-int. f f: -2, g: -1.5; slope g > slope f

20. Comparing Multiple Representations 9-4 3. A whale comes to the surface of the water at 80 ft/min from a depth of 1000 ft. Another whale ascends as shown in the table. Find and compare the rates of change and initial values of the linear functions in terms of the situations they model f(x) = 80x - 1000 Lesson Quiz : Part II Whale #2 started at -800 ft, which is 200 ft higher than Whale #1. Whale #2 ascends at 100 ft /min, which is 20 ft/min faster than Whale #1. Time (min) 0123 Depth (ft) -800-700-600-500

21. Comparing Multiple Representations 9-4 1. What slope is greater? f(x) = –3x + 5 A. f B. g Lesson Quiz for Student Response Systems

22. Comparing Multiple Representations 9-4 2. Which has the greater y-intercept? f(x) = –3x + 5 A. f B. g Lesson Quiz for Student Response Systems