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Name _______________________________________ Date _______________ Objective: 8M.3.2.1 Sketch and interpret a graph that models a given context, describe a context that is modeled by a given graph. ____________________________________________________ 1. Which path below would describe a race car that started slowly at first and gradually increased its speed? A. Y B. X C. W D. Z 2. You have 200 pounds of clay to use for making bowls and vases. You need 4 pounds of clay for each bowl and 2.5 pounds of clay for each vase. Which inequality represents the possible numbers of bowls and vases you can make? Graph the correct inequality. A. 4b + 2.5v < 200 B. 4b + 2.5v 200 C. 4v + 2.5b 200 D. 4b + 2.5v > 200 E. 4b + 2.5v 200 3. Billy ran up a hill. Billy's position changed horizontally 2 feet for every 1/2 foot of vertical change as he ran up the hill. Which graph below shows Billy's movement? A. X B. Y C. W D. Z 4. Marissa noticed that the price of chocolate milk at her school has increased at a constant rate since she was in first grade. Which of the following graphs accurately represents this situation? A. W B. X C. Y D. Z 5. You have a $100 gift card to a store that rents movies and video games. The rental fee for a movie is $4.00 and the rental fee for a video game is $5.00. Which inequality represents the possible numbers of movies and video games you can rent? Using intercepts, graph the correct inequality. A. 4m + 5v < 100 B. 4m + 5v 100 C. 5m + 4v 100 D. 4m + 5v > 100 E. 4m + 2.5v 100 8M.3.2.1 Key 1. 2. 3. 4. 5. D E C A B Explanations 1. Graph X shows a car that started off slow and then gradually increased its speed. As the car's acceleration increased, the slope of the line increased steeply, which created the curved line. Graph W shows a car that started fast and then slowed down. Graph Y shows a car that was stopped and then accelerated quickly. Graph Z shows a car that traveled at a constant speed. 2. The amount of clay that can be used is “less than or equal to” 200, the sign used must be > Let “b” represent the amount of clay needed for a bowl, and “v” the amount of clay needed for a base. The correct inequality is: 4b + 2.5v 200 Use the intercepts to determine two points on the graph. When b = 0, v = 80. When v = 0, b = 50. Connect the two points to create the graph, and shade in all the area in the quadrant beneath the line. 3. For every 2 feet that Billy runs horizontally (shown on x-axis), he runs 1/2 foot vertically (shown on y-axis). So, after running 4 feet horizontally, he would have run 1 foot vertically, and so on. Notice that graph W contains the point (4,1). This is a clue that graph W is correct. 4. In graph X, the price increases, but the grade decreases. Therefore, X is not the correct graph. In graph Y, the price increases, but does not increase at a constant rate. Therefore, Y is not the correct graph. In graph Z, the price increases, but does not increase at a constant rate. Therefore, Z is not the correct graph. In graph W, the price increases at a constant rate as her grade increases. Therefore, W is the correct graph. 5. The amount of money that can be used is “less than or equal to” $100, the sign used must be > . Let “m” represent the rental cost of a movie, and “v” the rental cost of a video game. The correct inequality is: 4m + 5v $100 Use the intercepts to determine two points on the graph. When m = 0, v = 20. When v = 0, m = 25. Connect the two points to create the graph, and shade in all the area in the quadrant beneath the line.