Name: ____________________________ Ratios and Proportions – Unit Rate and Constant Rate of Change 1 The table below shows the number of pages Adriano read in x hours. 3 Date: _________ PreAlgebra Sheet # 02 - 13 The table and graph below show the hourly charge to rent a bicycle at two different stores. Part A Graph the data then determine the slope of the line. Part B Discuss what the slope means as the constant rate of change. Which store charges more per hour? Explain. Part C What does the ordered pair (1, 50) represent? Is this the constant unit rate? Explain why or why not. 2 The table below shows the relationship between the number of feet and the number of yards. 4 The table, graph, and equation below show the amount of money Mi-Ling, Daniel, and Sebastian save each week. Part A Graph the data then determine the slope of the line. Sebastian’s Savings y = 5x Part A Who saves more each week? Explain. Part B Discuss what the slope means as the constant rate of change. Part C What does the ordered pair (1, 3) represent? Is this the constant unit rate? Explain why or why not. Part B Refer to the graph of Daniel’s Savings. Explain what the points (0, 0) and (1, 10) represent. 5 The Guzman, Hashimoto, and Castellano families each took a 4-hour road trip. The distances traveled by each family are shown in the table, graph, and equation below. Castellano’s Road Trip 8 9 y = 50 x Taxi cab passengers are charged $2.50 upon entering a cab. They are then charged $1.00 for every mile travelled. Is the cost to miles travelled a proportional relationship? Explain. A restaurant charges $5 for one sandwich, $9.90 for two sandwiches, and $14.25 for three sandwiches. Is the cost to number of sandwiches a proportional relationship? Explain. Which family averaged fewer miles per hour? Explain. 6 The table shows the cost to rent a paddle boat from two businesses. 10 The graph below shows the proportional relationship between x, the number of eggs used in an egg casserole, and y, the number of servings in the casserole. Part A What does (1, 20) represent? Which equation describes the proportional relationship shown above? Part B What does (2, 50) represent? 7 The graph below shows the distance David traveled while jogging. Find David’s constant rate of change in feet per second. 11 A y= 3 x 2 C y= 2 x 3 B y= 3 x +1 2 D y= 2 x +1 3 A garden hose leaks 3 1 gallon of water in hour. 8 4 At this rate, how many gallons of water will the hose leak in 1 hour? A 3 gallon 32 C 3 1 gallons 8 B 5 gallon 8 D 1 1 gallons 2