You need two points to calculate slope. Algebra 1B – Name: _________________________ Section 4.4 Slope & Rate of Change Date: __________________________ Objective: Calculate, identify and interpret slope of a line. The slope of a line is the ___________________________________________________ ____________________________________________________________________________________________________________________________________________ Slope of this skateboarding ramp: ______________________ You need two points to calculate slope. The formula is: We will use this formula often. It will be on the Algebra 1 formula sheet. Example 1: Example 2: Example 3: Page 1

Page 2 Types of Slopes Positive Negative Zero Undefined p. 230 #20

Rate of Change: Compares two different quantities that are changing. A ball rolls down a ramp with a slope of 2/3. At one point the ball is 10 feet high, and at another point the ball is 4 feet high, as shown in the diagram below. What is the horizontal distance (x), in feet, the ball traveled as it rolled down the ramp from 10 feet high to 4 feet high? A) B) C) D) Rate of Change: Compares two different quantities that are changing. Example: You are parachuting. At time t = 0 seconds, you open your parachute at height h = 2500 feet above the ground. At time t = 35 seconds, you are at height h = 2115 feet. What is your rate of change? About when will you reach the ground? Page 3

Page 4 Distance = Rate x Time Ahava is traveling on a train. The train is going at a constant speed of 80 miles per hour. A. How many hours will it take for the train to travel 1,120 miles? Ahava also considered taking an airplane. The airplane can travel the same 1,120 miles in 12 hours less time than the train. B. What is the speed of the airplane in miles per hour (mph)? p. 232 #56. A space shuttle achieves orbit at 9:23 A.M. At 9:31 A.M. it has traveled 2,309.6 miles in orbit. Find the rate of change in miles per minute. p. 232 #57. In 1990, a company had a profit of $173,000,000. In 1996, the profit was $206,000,000. If the profit increased the same amount each year, find the rate of change of the company's profit in dollar per year. p. 231 #51. The U.S. Department of Transportation requires surveyors to place signs on steep sections of roads. The grade of a road is measured as a percent. For instance, the grade of the road shown below is 6%. What is the slope of the road? Explain the relationship between road grade and slope. Page 4

Each week a salesman makes $500 as a base salary Each week a salesman makes $500 as a base salary. He also earns $50 for each sale that he makes. 1) Write an equation to model the salesman's salary for the week. f(s) = f(s) is his salary; s is the number of sales he makes. 2) What is the slope and what does it mean? _____________________________________________________________________ _____________________________________________________________________ 3) What will be the salesman's salary if he makes 7 sales during the week? For each hour of exercise, Melissa burns 300 calories. 1) Write an equation to model the amount of calories that Melissa burns. Let C be number of calories and t be the number of hours. C(t) = 2) What is the slope and what does it mean? __________________________________________________________________________________________________________________________________________ 3) How many calories does Melissa burn after... a) 2 Hours? b) 90 Minutes? c) 0 Hours? A pizza restaurant charges for pizzas and adds a delivery fee. The cost (c), in dollars, to have any number of pizzas (p) delivered to a home is described by the function c = 8p + 3. Which statement is true? A. The cost of ____________________________ B. The cost of ____________________________ C. Each pizza costs ______________________________ D. Each pizza costs ______________________________ Page 5

p. 232 #58-61 The graph shows the price of a movie ticket at the Midtown Theater for the years 1960-1995. 58) Estimate the rate of change from 1960 to 1995 in the price in dollars per year. 59) Estimate the rate of change from 1985 to 1990 in the price in dollars per year. 60) Which five year period had the smallest price increase? 61) Use the graph to estimate the cost of going to a movie at the Midtown Theater this year Why might your estimate be different from the actual cost? Jenny has a job that pays her $8 per hour plus tips (t). Jenny worked for 4 hours on Monday and made $65 in all. Which equation could be used to find t, the amount Jenny made in tips? A) B) C) D) Nolan has $15.00, and he earns $6.00 an hour babysitting. The equation below can be used to determine how much money in dollars (m) Nolan has after any number of hours of babysitting (h). After how many hours of babysitting will Nolan have $51.00? Page 6