Name Class Date. Comparing Multiple Representations Going Deeper. Comparing a Table and a Graph

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1 1 Name Class Date Comparing Multiple Representations Going Deeper Essential question: How can ou use tables, graphs, and equations to compare functions? CC.8.EE.5 EXPLORE Comparing a Table and a Graph 9-4 video tutor The table and graph show how man words Morgan and Brian tped correctl on a tping test. For both students, the relationship between words tped correctl and time is linear. Brian s Tping Test Morgan s Tping Test Time (min) Words A Find Morgan s unit rate. Words B Find Brian s unit rate Time (min) 10 C Which student tpes more correct words per minute? REFLECT 1a. Sketch a graph of Morgan s test results on the same coordinate grid as Brian s results. How are the graphs similar? How are the different? 1b. Katie tpes 17 correct words per minute. Eplain how a graph of Katie s test results would compare to Morgan s and Brian s. 1c. The equation that describes Jen s test results is = 24. Eplain how a graph of Jen s test results would compare to Morgan s and Brian s. Chapter Lesson 4

2 2 CC.8.F.2 eplore Comparing a Table and an Equation Josh and Maggie bu MP3 files from different music download services. With both services, the monthl charge is a linear function of the number of songs downloaded. The cost at Josh s service is described b = where is the cost in dollars and is the number of songs downloaded. Cost of MP3s at Maggie s Music Service Songs, Cost ($), A Find the unit rate of each function. Josh: Maggie: B Which function has the greater rate of change? What does that mean in this contet? C Write an equation in slope-intercept form to describe the cost at Maggie s music service. = m + b = + b Substitute for, m, and. = + b Subtract the number that is added to b from both sides. - - = b = + D Describe each service s cost in words using the meanings of the slopes and -intercepts. REFLECT 2a. How much does it cost at each service to download 20 songs? 2b. You are tring to choose between these two music services. How could ou decide which service is better for ou? Chapter Lesson 4

3 3 CC.8.F.4 EXplore Comparing a Graph and a Description Jamal wants to bu a new game sstem that costs $200. He onl has $100 toda, so he compares laawa plans at different stores. The plan at Store A is shown on the graph. Store B requires an initial pament of $60 and weekl paments of $20 until the balance is paid in full. Balance Owed ($) A Use the graph of the laawa plan at Store A to write an equation in slope-intercept form. Let represent number of weeks and represent balance owed Number of Weeks 10 B Use the description of the laawa plan at Store B to write an equation in slope-intercept form. Let represent number of weeks and represent balance owed. C Sketch a graph of the plan at Store B on the same grid as Store A. D How can ou use the graphs to tell which plan requires the greater down pament? How can ou use the equations? E How can ou use the graphs to tell which plan requires the greater weekl pament? How can ou use the equations? F Which plan allows Jamal to pa for the game sstem faster? Eplain. Chapter Lesson 4

4 practice The table and the graph displa two different linear functions. Input, Output, Find the slope of each function. Table: Graph: 2. Without graphing the function represented in the table, tell which function s graph is steeper. 3. Write an equation for each function. Table: Graph: 4. Use the equations from 3 to tell which function has the greater -intercept. Aisha runs a tutoring business. Students ma choose to pa $15 per hour or the ma follow the plan shown on the graph. 5. Describe the plan shown on the graph. 6. Sketch a graph showing the $15 per hour option. 7. What does the intersection of the two graphs mean? Cost ($) Time (hr) 8. If ou wanted to hire Aisha for tutoring, how can ou decide which pament option is better for ou? Chapter Lesson 4

5 Name Class Date 9-4 Additional Practice 1. Find and compare the slopes for the linear functions f and g. f() g() slope of f slope of g Compare 2. Find and compare the -intercepts for the linear functions f and g f() intercept of f -intercept of g Compare O g() Connor and Sheila are in a rock-climbing club. The are climbing down a canon wall. Connor starts from a cliff that is 200 feet above the canon floor and climbs down at an average speed of 10 feet per minute. Sheila climbs down the canon wall as shown in the table. Time (min) Sheila s height (ft) Interpret the rates of change and initial values of the linear functions in terms of the situations the model. Connor Sheila Initial value Initial value Rate of change Rate of change Compare Chapter Practice and Problem Solving

6 Problem Solving Find and compare the rates of change and initial values of the linear functions in terms of the situations the model. 1. Dan and Keri assemble biccles. So far toda, Dan has assembled 3 bikes. He works at a rate of 0.5 bikes per hour. Keri has assembled 4 bikes, so far toda, and assembles biccles as shown in the table. 2. Javier and Wend pa for their cell phone service from their checking accounts according to the equation and graph shown. Javier: f() Wend Time (hr) Bikes Keri Assembled Account balance ($) O Time (months) Use the table and the graph for Eercises 3 and 4. Choose the letter for the best answer. Jane and Ale each start driving from their homes, which are different distances from the warehouse where the both work, to a meeting out of town. Jane Time (hr) Distance (mi) How much farther from the warehouse was Jane than Ale when she started driving toda? A 50 miles C 75 miles B 60 miles D 200 miles Distance (mi) Ale Time (hr) 4. How much faster is Jane driving than Ale? A 55 miles per hour B 50 miles per hour C 25 miles per hour D 5 miles per hour O Chapter Practice and Problem Solving