Warm Up Problem of the Day Lesson Presentation Lesson Quizzes
Warm Up 1. Find the slope of a line through points (3, 4) and (6, 2). -2 3 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
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).
Learn to compare linear functions represented in different ways.
Helpful Hint Remember that slope is rise (change in y) divided by run (change in x) or rise over run.
Additional Example 1: Comparing Slopes Find and compare the slopes for the linear functions f and g. f(x) = 10x 5 x 2 1 0 1 g(x) 0 5 10 15 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.
Additional Example 1: Continued Find the slope of g. m = y 2 y 1 x 2 x 1 10 5 = = 5 0 ( 1) The slope of g is 5. The slope f is greater than the slope of g.
Check It Out: Example 1 Find and compare the slopes for the linear functions f and g. f(x) = 8x + 4 x 2 1 0 1 g(x) 0 8 16 24 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.
Continued: Check It Out Example 1 Find the slope of g. m = y 2 y 1 x 2 x 1 16 8 = = 8 0 ( 1) The slope of g is 8. The slope f is the same as the slope of g.
Additional Example 2: Comparing Intercepts Find and compare the y-intercepts for the linear functions f and g. x 0 1 2 3 f(x) -6-4 -2 0 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. The graph of g crosses the y- axis at about 5. The y-intercept of g is greater than the y-intercept of f.
Check It Out: Example 2 x 1 0 1 2 f(x) 0 3 6 9 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.
Remember! Rate of change is given by the slope and initial value is given by the y-intercept of a linear function.
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 Time (sec) 0 1 2 3 Height (ft) 575 565 555 545 Fred s descent. f(x) = mx + b f(x) = 15x +700 The rate of change is 15. The initial value is 700.
Additional Example 3: Continued Gene s descent. m = y 2 y 1 x 2 x 1 = = 10 565 575 1 0 The rate of change is 10. 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.
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) Height (ft) 0 1 2 3 480 465 450 435
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.
Continued: Check It Out Example 3 Gene s descent. m = y 2 y 1 x 2 x 1 = = 15 465 480 1 0 The rate of change is 15. 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.
Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems
Lesson Quiz : Part I 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. f: -2, g: -1.5; slope g > slope f 2. Find and compare the y-intercepts for the linear functions f and g. f: 3, g: 4; y-int. g > y-int. f
Lesson Quiz : Part II 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 Time (min) Depth (ft) 0 1 2 3-800 -700-600 -500 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.
Lesson Quiz for Student Response Systems 1. What slope is greater? f(x) = 3x + 5 A. f B. g
Lesson Quiz for Student Response Systems 2. Which has the greater y-intercept? f(x) = 3x + 5 A. f B. g