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October 02, 2013 2-2 Proportional Relationships, Tables, and Equations October 02, 2013 Essential Question: How can you use tables and equations to identify and describe proportional relationships? October 02, 2013 Discovering proportional relationships A giant tortoise moves at a slow but steady pace. It takes the tortoise 3 seconds to travel 10.5 inches. Use the bar diagram to help determine how fast it goes in one second. What operation did you use to find your answer? October 02, 2013 Complete the table: Time (sec) 1 2 3 4 5 Distance (in) Find the ratio of distance to time. Write each ratio in simplest form. What do you notice about the ratios? How do you think the distance a tortoise travels is related to time? October 02, 2013 Complete the table: Time (sec) 1 2 3 4 5 Distance (in) Find the ratio of distance to time. Write each ratio in simplest form. What do you notice about the ratios? How do you think the distance a tortoise travels is related to time? October 02, 2013 Suppose the tortoise travels for 12 seconds. Explain how you could find the distance the tortoise travels. How would you describe the rate or speed at which the tortoise travels? October 02, 2013 PROPORTIONAL relationship is a relationship between two quantities in which the ratio of one quantity to another is constant. October 02, 2013 Alberto types 45 words per minute. Is the relationship between the number of words and the number of minutes a proportional relationship? Why or why not? Time (min) 1 2 3 Number 45 of words Compete the ratios of words minutes constant the ratios are __________ 45 The common ratio is :__________ proportional So the relationship is ___________ 4 5 October 02, 2013 The table shows the distance Allison drove on each day of her vacation. Is the relationship between the distance and the time a proportional relationship? Why or why not? Time(h) 1 Distance 65 (mi) 2 3 4 5 120 195 220 300 Do you think Allison drove at a constant speed for the entire trip? Why or why not? October 02, 2013 Equations for proportional relationships: y = ax October 02, 2013 Two pounds of cashews cost $5, 3 pounds of cashews cost $7.50, and 8 pounds of cashews cost $20. Show that the relationship between the number of pounds of cashews and the cost is a proportional relationship. Then, write the equation for that relationship. a) table pounds 2 cost ($) 5 3 b) ratios 2.5 The common ratio is: _______ c) Write the equation: 8 October 02, 2013 How can you use substitution to check your equation? What is the unit cost (unit rate) for the cashews? How does the unit cost appear in your equation? How can you use your equation to find the cost of 6 pounds of cashews? October 02, 2013 Journal: 1)How can you use tables and equations to identify and describe proportional relationships? 2) Create a graphic organizer like the one below to show how we can use tables and equations to model proportional relationships. We will be adding to it in the coming sections. words equation proportional relationships table Graph