Intermediate Algebra – Student Workbook – Second Edition 2013

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$Lesson 2a – Assessment - Scottsdale Community College - Math Blog$

Lesson 2a – Linear Functions and Applications Mini-Lesson Problem 9 WORKED EXAMPLE – Multiple Ways to Determine The Equation of a Line Determine if the data below represent a linear function. If so, use at least two different methods to determine the equation that best fits the given data. x 1 5 9 13 y 75 275 475 675 Compute a few slopes to determine if the data are linear. 275 75 200 Between (1, 75) and (5, 275) m 50 5 1 4 475 275 200 Between (5, 275) and (9, 475) m 50 9 5 4 675 475 200 Between (9, 475 and 13, 675) m 50 13 9 4 The data appear to be linear with a slope of 50. Method 1 to determine Linear Equation – Slope Intercept Linear Form (y = mx + b): Use the slope, m = 50, and one ordered pair, say (1, 75) to find the y-intercept 75 = 50(1) + b, so b=25. Thus the equation is given by y = 50x + 25. Method 2 to determine Linear Equation – Linear Regression: Use the steps for Linear Regression to find the equation. The steps can be used even if the data are exactly linear. Step 1: Go to STAT>EDIT>1:Edit Step 2: Clear L1 by scrolling to L1 then press CLEAR then scroll back down one row Step 3: Enter the values 1, 5, 9, 13 into the rows of L1 (pressing Enter between each one) Step 4: Right arrow then up arrow to top of L2 and Clear L2 by pressing CLEAR then scroll back down Step 5: Enter the values 75, 275, 475, 675 into the rows of L2 (pressing Enter between each one) Step 6: Go to STAT>EDIT>CALC>4:LinReg (ax + b) then press ENTER twice Step 7: Read the values a and b from the screen and use them to write the equation, y = 50x + 25 Scottsdale Community College Page 64 Intermediate Algebra
Name: _____________________ Date: ________________ Lesson 2a Practice Problems 1. The data below represent the number of times your friends embarrassing YouTube Video has been viewed per hour since you uploaded it. The data are exactly linear. Time, t, in hours 0 1 2 3 4 Views, V, in thousands 0 6200 12400 18600 24800 a) Identify the vertical intercept and average rate of change for the data, then use these to write the linear function model for the data. Use the indicated variables and proper function notation. b) Use your model to determine the number of views in hour 8. Write your final result as a complete sentence. c) Use your model to determine how many hours until the number of views reaches 100,000. Round to the nearest whole year. Write your final result as a complete sentence. 2. You adopted an adult cat four years ago. The data below represent your cat’s weight for four years she’s lived with you. The data are exactly linear. Time, t, in years 0 1 2 3 4 Weight, W, in pounds 6 7.25 8.5 9.75 11 a) Identify the vertical intercept and average rate of change for the data, then use these to write the linear function model for the data. Use the indicated variables and proper function notation. Scottsdale Community College Page 65 Intermediate Algebra
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Scottsdale Community College Interm
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Table of Contents Lesson 1a - Intro
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Lesson 1a - Introduction to Functio
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Lesson 6a - Exponents and Rational
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Lesson 6b - Rational Exponents & Ra
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Lesson 6b - Rational Exponents and
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Appendix A: You Try Answers Lesson
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Appendix A: You Try Answers You Try
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Intermediate Algebra – Student Workbook – Second Edition 2013

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