Algebra 1 Unit 3: Writing Equations
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1 Lesson 8: Making Predictions and Creating Scatter Plots The table below represents the cost of a car over the recent years. Year Cost of a Car (in US dollars) , , , , , , ,000 Create a scatter plot to display the data. Create a line of best fit that can be used to make predictions. Write an equation for the line of best fit. Making Predictions 1. Based on your line of best fit, what does the slope and y-intercept represent? 2. Based on the line of best fit, what will be the cost of the car in the year 2015? Justify your answer. 3. Predict the cost of the car for the year Do you think this is a good prediction?
2 Example #2 The table shows the median selling price of a new single family home in the Washington DC area. (As per Trulia.com) Make a scatter plot of the data. Year Median Price 2000 $130, $200, $300, $400, $410, $380,000 Use the graphing calculator to write an equation for the line of best fit. Draw the line of best fit on your graph. Making Predictions 1. Based on your line of best fit, what does the slope and y-intercept represent? 2. Predict the median price of a new single family home in DC for the year Predict the median price of a new single family home in DC for the year 2020.
3 Lesson 8: Making Predictions and Creating Scatter Plots Practice Problems Directions: For each of the problem below, complete the following: Create a scatter plot. Write an equation for the line of best fit. (You may either use the graphing calculator, or draw your own line of best fit and write an equation.) Use the line of best fit to predict the missing value in the table. Use the line of best fit to answer the remaining questions. 1. The table below represents the number of dogs in the US from the year 2000 to 2008 (in millions).(information taken from Statista.com) Year # of Dogs in Millions ? Use the line of best fit to predict the number of dogs in the US in the year 2020.
4 2. The table below represents the number of hours a typical person spends watching TV per year from the year 2002 to 2010 (Information taken from statista.com). Year # of Hours spend watching TV ? What does the slope and y-intercept represent in the equation for the line of best fit?
5 3. The table below represents the total amount of computer/video game sales in the US (in billions of dollars).(information taken from Statista.com) Year Total amount of computer/video game sales in US ? Use the line of best fit to predict number of computer/video game sales in the year Analyze the following data on your graphing calculator. Determine whether you will be able to accurately find an equation for the line of best fit for this data to make predictions. Explain your reasoning. The table below represents the number of fresh water fish in the US (in millions). Year Number of Fresh Water Fish in US (in millions)
6 Lisa has $500 to invest in stock. She is deciding between two different companies to invest her money in for a long term basis. The stock prices for each company, for the first 6 months of the year are shown in the table below. Month January February March April May June Company Company Write an equation for the line of best fit for both companies. Based on the line of best fit, how much will Company 1 s stock cost at the end of the year? Based on your equation for the line of best fit, which company should Lisa invest her money in if she were going to invest for 13 months (starting with January as the first month)? Based on your equation for the line of best fit, which company should Lisa invest her money in if she were going to invest for 2 years (starting with January as the first month)?
7 Lesson 8: Making Predictions and Creating Scatter Plots Practice Problems Answer Key Directions: For each of the problem below, complete the following: Create a scatter plot. Write an equation for the line of best fit. (You may either use the graphing calculator, or draw your own line of best fit and write an equation.) Use the line of best fit to predict the missing value in the table. Use the line of best fit to answer the remaining questions. 1. The table below represents the number of dogs in the US from the year 2000 to 2008 (in millions).(information taken from Statista.com) Year # of Dogs in Millions ? The line of best for this set of data is: Y = 1.35x Number of Dogs in the US Use the line of best fit to predict the number of dogs in the US in the year Y = 1.35x Y = 1.35(20) Y = 93.2 There will be about 93 million dogs in the US in the year (I substituted 20 for x since 2020 is 20 years later than 2000.
8 2. The table below represents the number of hours a typical person spends watching TV per year from the year 2002 to 2010 (Information taken from statista.com). Year # of Hours spend watching TV ? The line of best for this set of data is: Y = 25x Y = 25x Y = 25(12) Y = People will spend about 1,083 hours watching TV in the year (I substituted 12 for x since 2012 is 12 years later than 2000 which is where I chose to start my graph. What does the slope and y-intercept represent in the equation for the line of best fit? The slope, 25, represents how many more hours per year a person will watch TV. So, each year, a person s TV viewing increases by 25 hours. The y-intercept represents how many hours people watched TV per year in the year We don t have data to represent this, but we can tell from our line of best fit, that approximately, 783 hours were spent watching TV per person in the year 2000.
9 3. The table below represents the total amount of computer/video game sales in the US (in billions of dollars).(information taken from Statista.com) Year Total amount of computer/video game sales in US ? The line of best for this set of data is: Y = 1.02x Y = 1.02x+4.17 Y = 1.02(12)+4.17 Y = About billion in sales were made on computer/video games in the year (I substituted 12 for x since the year 2012 is 12 years later than the year 2000.) Use the line of best fit to predict number of computer/video game sales in the year Y = 1.02x+4.17 Y = 1.02(15)+4.17 Y =19.47 About billion in sales were made on computer/video games in the year (I substituted 15 for x since the year 2015 is 15 years later than the year 2000.) 14. Analyze the following data on your graphing calculator. Determine whether you will be able to accurately find an equation for the line of best fit for this data to make predictions. Explain your reasoning. The table below represents the number of fresh water fish in the US (in millions). Year Number of Fresh Water Fish in US (in millions) This data does not show a linear pattern. The points are more scattered and a straight line would not accurately describe the data. Therefore, an equation for a line of best fit would not accurately allow predictions to be made for this set of data.
10 Lisa has $500 to invest in stock. She is deciding between two different companies to invest her money in for a long term basis. The stock prices for each company, for the first 6 months of the year are shown in the table below. Month January February March April May June Company Company Write an equation for the line of best fit for both companies. (2 points) (I used the stat and linear regression functions on the graphing calculator to write an equation for the line of best fit.) Company #1: y = 3.09x Company #2: y = 2.65x Based on the line of best fit, how much will Company 1 s stock cost at the end of the year? (2 points) Based on the line of best fit, Company1 s stock will cost: $62.95 at the end of the year. Y=3.09x Company 1 s equation. Y = 3.09(12) The end of the year will be the 12 th month. Substitute 12 for x. Y = Company 1 s stock will cost approximately $62.95 at the end of the year. Based on your equation for the line of best fit, which company should Lisa invest her money in if she were going to invest for 13 months (starting with January as the first month)? (2 points) Company 1: y = 3.09x Company 2: y = 2.65x Y = 3.09(13) y = 2.65(13) Y = y = Company 2 will cost more per share, so she should invest in Company number 2 if she is going to invest for 13 months. Based on your equation for the line of best fit, which company should Lisa invest her money in if she were going to invest for 2 years (starting with January as the first month)? (2 points) Since our equation is based on months, we need to substitute 24 for x since 2 years is 24 months. Company 1: y = 3.09x Company 2: y = 2.65x Y = 3.09(24) y = 2.65(24) Y = y = Company 1 will cost more per share, so she should invest in Company number 1 if she is going to invest for 2 years.
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