Is It Getting Hot in Here?

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1 Lesson.1 Skills Practice Name Date Is It Getting Hot in Here? Modeling Data Using Linear Regression Vocabulary Choose the term that best completes each sentence. linear regression line of best fit linear regression equation significant digits correlation coefficient 1. The equation that describes a line of best fit is called a linear regression equation. 2. Decimal digits that carry meaning contributing to a number s precision are significant digits.. Linear regression producing a line of best fit. models the relationship between two variables in a data set by 4. A line of best fit is a line that best approximates the linear relationship between two variables in a data set. 5. The correlation coefficient indicates how closely data points are to forming a straight line. Chapter Skills Practice 25

2 Lesson.1 Skills Practice page 2 Problem Set Use your calculator to determine the linear regression equation and the correlation coefficient for each given set of data. Then use the equation to make the prediction. 1. The table shows the attendance for the varsity football games at Pedro s high school. Predict the attendance for Game 9. Game Attendance f(x) 5 7x 1 196, r Game 1 is represented by x 5 1, so Game 9 is represented by x 5 9. f(x) 5 7x f(9) 5 7(9) f(9) The attendance during Game 9 will be 2620 people. 26 Chapter Skills Practice

3 Lesson.1 Skills Practice page Name Date 2. The table shows the attendance for the annual spring concert at Eva s high school for 6 years. Predict the attendance in Year Attendance f(x) 5 25x 1 771, r The year 2007 is represented by x 5 0, so the year 2016 is represented by x 5 9. f(x) 5 25x f(9) 5 25(9) f(9) For the 2016 spring concert, 996 people will be in attendance. Chapter Skills Practice 27

4 Lesson.1 Skills Practice page 4. The table shows the average gas price for 6 months. Predict the average gas price for August. Month Price of Gas (dollars) January $.15 February $.22 March $.19 April $.28 May $.5 June $.2 f(x) x 1.12, r January is represented by x 5 1, so August is represented by x 5 8. f(x) x 1.12 f(8) (8) 1.12 f(8) 5.44 The average price of gas in August will be $ Chapter Skills Practice

5 Lesson.1 Skills Practice page 5 Name Date 4. The table shows monthly record sales of a recording artist over 6 months. Predict the record sales total for December. Monthly Record Sales (CDs) January 60,000 February 54,000 March 58,000 April 46,000 May 4,000 June 0,000 f(x) x 1 68,000, r January is represented by x 5 1, so December is represented by x f(x) x 1 68,000 f(12) (12) 1 68,000 f(12) The record sales for December will be 1148 CDs. Chapter Skills Practice 29

6 Lesson.1 Skills Practice page 6 5. The table shows the number of miles Kata traveled for work each year for 6 years. Predict the number of miles Kata will travel in Year Miles Traveled f(x) 5 25x 1 80, r The year 2006 is represented by x 5 0, so the year 2014 is represented by x 5 8. f(x) 5 25x 1 80 f(8) 5 25(8) 1 80 f(8) In 2014, Kata will travel 562 miles. 0 Chapter Skills Practice

7 Lesson.1 Skills Practice page 7 Name Date 6. The table shows the number of songs downloaded for a recording artist over 6 months. Predict the number of songs that will be downloaded in November. Month Songs Downloaded January 15,02 February 16,78 March 18,204 April 17,899 May 20,45 June 24,980 f(x) x 1 1,042, r January is represented by x 5 1, so November is represented by x f(x) x 1 1,042 f(11) (11) 1 1,042 f(11) 5 1,511 In November, 1,511 songs will be downloaded. Chapter Skills Practice 1

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9 Lesson.2 Skills Practice Name Date Tickets for Sale Standard Form of Linear Equations Vocabulary Define each term in your own words. 1. standard form The standard form of a linear equation is Ax 1 By 5 C where A, B, and C are constants and A and B are not both zero. 2. slope-intercept form The slope-intercept form of a linear equation is y 5 mx 1 b where b is the y-intercept and m is the slope. Problem Set Define variables and write an expression to represent each situation. 1. A farmer s market sells apples for $0.75 per pound and oranges for $0.89 per pound. Write an expression to represent the total amount the farmer s market can earn selling apples and oranges. a 5 pounds of apples b 5 pounds of oranges 0.75a b 2. A photo printing website sells 8 10 prints for $4.99 and 5 prints for $1.99. Write an expression to represent the total amount the website can earn selling 8 10 and 5 prints. c prints d 5 5 prints 4.99c d. A movie theater sells tickets for matinee showings for $7.00 and evening showings for $ Write an expression that represents the total amount the theater can earn selling tickets. m 5 matinee n 5 evening 7m n Chapter Skills Practice

10 Lesson.2 Skills Practice page 2 4. A bakery sells muffins for $1.25 each and scones for $1.75 each. Write an expression that represents the total amount the bakery can earn selling muffins and scones. x 5 muffins y 5 scones 1.25x y 5. A florist sells daisies for $8.99 a dozen and roses for $15.99 a dozen. Write an expression that represents the total amount the florist can earn selling daisies and roses. d 5 daisies r 5 roses 8.99d r 6. The hockey booster club is selling winter hats for $12 each and sweatshirts for $26 each. Write an expression that represents the total amount the booster club can earn selling hats and sweatshirts. h 5 hats s 5 sweatshirts 12h 1 26s Define variables and write an equation to represent each situation. 7. A florist sells carnations for $10.99 a dozen and lilies for $12.99 a dozen. During a weekend sale, the florist s goal is to earn $650. Write an equation that represents the total amount the florist would like to earn selling carnations and lilies during the weekend sale. c 5 carnations f 5 lilies 10.99c f A bakery sells bagels for $0.85 each and muffins for $1.10 each. The bakery hopes to earn $400 each day from these sales. Write an equation that represents the total amount the bakery would like to earn selling bagels and muffins each day. b 5 bagels m 5 muffins 0.85b 1 1.1m A farmer s market sells oranges for $0.79 per pound and peaches for $1.05 per pound. The farmer s market hopes to earn $25 each day from these sales. Write an equation to represent the total amount the farmer s market would like to earn selling oranges and peaches each day. q 5 pounds of oranges r 5 pounds of peaches 0.79q r Chapter Skills Practice

11 Lesson.2 Skills Practice page Name Date 10. The high school soccer booster club sells tickets to the varsity matches for $4 for students and $8 for adults. The booster club hopes to earn $200 at each match. Write an equation to represent the total amount the booster club would like to earn from ticket sales at each match. s 5 students a 5 adults 4s 1 8a An electronics store sells DVDs for $15.99 and Blu-ray discs for $ The store hopes to earn $2000 each week from these sales. Write an equation to represent the total amount the store would like to earn each week. d 5 DVDs b 5 Blu-ray discs 15.99d b Ling is selling jewelry at a craft fair. She sells earrings for $5 each and bracelets for $7 each. She hopes to earn $00 during the fair. Write an equation to represent the total amount Ling would like to earn during the fair. e 5 earrings b 5 bracelets 5e 1 7b 5 00 The basketball booster club runs the concession stand during a weekend tournament. They sell hamburgers for $2.50 each and hot dogs for $1.50 each. They hope to earn $900 during the tournament. The equation 2.50b h represents the total amount the booster club hopes to earn. Use this equation to determine each unknown value. 1. If the booster club sells 15 hamburgers during the tournament, how many hot dogs must they sell to reach their goal? 2.50b h (15) h h h h 5 75 The booster club must sell 75 hot dogs to reach their goal. Chapter Skills Practice 5

12 Lesson.2 Skills Practice page If the booster club sells 420 hot dogs during the tournament, how many hamburgers must they sell to reach their goal? 2.50b h b (420) b b b The booster club must sell 108 hamburgers to reach their goal. 15. If the booster club sells 0 hot dogs during the tournament, how many hamburgers must they sell to reach their goal? 2.50b h b (0) b b 5 60 The booster club must sell 60 hamburgers to reach their goal. 16. If the booster club sells 0 hamburgers during the tournament, how many hot dogs must they sell to reach their goal? 2.50b h (0) h h h The booster club must sell 600 hot dogs to reach their goal. 17. If the booster club sells 281 hamburgers during the tournament, how many hot dogs must they sell to reach their goal? 2.50b h (281) h h h h The booster club must sell 12 hot dogs to reach their goal. 6 Chapter Skills Practice

13 Lesson.2 Skills Practice page 5 Name Date 18. If the booster club sells 168 hot dogs during the tournament, how many hamburgers must they sell to reach their goal? 2.50b h b (168) b b b The booster club must sell 260 hamburgers to reach their goal. Determine the x-intercept and the y-intercept of each equation x 1 8y x 1 8y x 1 8(0) x x x 1 8y (0) 1 8y y y 5 0 The x-intercept is (12, 0) and the y-intercept is (0, 0) x 1 y x 1 y x 1 (0) x x x 1 y (0) 1 y y y 5 90 The x-intercept is (18, 0) and the y-intercept is (0, 90). 21. y 5 8x y 5 8x x x x The x-intercept is (221, 0) and the y-intercept is (0, 168). y 5 8x y 5 8(0) y Chapter Skills Practice 7

14 Lesson.2 Skills Practice page y 5 24x 1 52 y 5 24x x x 1 5 x y 5 24x 1 52 y 5 24(0) 1 52 y 5 52 The x-intercept is (1, 0) and the y-intercept is (0, 52) x 1 25y x 1 25y x 1 25(0) x 5 42 x x 1 25y (0) 1 25y y 5 42 y The x-intercept is approximately (24.4, 0) and the y-intercept is (0, 1.68). 24. y 5 6x y 5 6x y 5 6x x y 5 6(0) x y x The x-intercept is (248.5, 0) and the y-intercept is (0, 291). Determine the x-intercept and y-intercept. Then graph each equation x 1 6y x 2 9y 5 6 y y x x 5x 1 6y x 1 6y x 2 9y x 2 9y 5 6 5x 1 6(0) x (0) 1 6y y x 2 9(0) x (0) 2 9y y 5 6 x 5 18 y 5 15 x 5 y Chapter Skills Practice

15 Lesson.2 Skills Practice page 7 Name Date 27. y 5 x y 5 20x y y x x y 5 x 2 15 y 5 x 2 15 y 5 20x y 5 20x x 2 15 y 5 (0) x y 5 20(0) x y x y x 6 5 x 29. 6x 1 1y y 5 x 2 41 y y x x 6x 1 1y x 1 1y 5 57 y 5 x 2 41 y 5 x x 1 1(0) (0) 1 1y x 2 41 y 5 (0) x y x y x y x Chapter Skills Practice 9

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17 Lesson. Skills Practice Name Date Cool As A Cucumber or Hot Like A Tamale! Literal Equations in Standard Form and Slope-Intercept Form Vocabulary Define the term in your own words. 1. literal equations Literal equations are equations that are comprised of several variables. Problem Set Convert between degrees Fahrenheit and degrees Celsius using the literal equation given. If necessary, round the answer to the nearest hundredth. C 5 5 (F 2 2) F 5 C 5 (F 2 2) 9 5 C 5 (72 2 2) 9 5 C 5 9 (40) C F C F 5 C 5 (F 2 2) 9 5 C 5 [(211) 2 2] 9 5 C 5 9 (24) C F C F 5 C 5 (F 2 2) 9 5 C 5 ( ) 9 5 C 5 9 (70.6) C F 9.22 C C 5 C 5 5 (F 2 2) (F 2 2) 9 25 ( 9 5 ) 5 ( 9 5 ) 5 (F 2 2) (F 2 2) 77 5 F 25 C 5 77 F Chapter Skills Practice 41

18 Lesson. Skills Practice page C 5 C 5 (F 2 2) ( 9 5 ) 5 ( 9 (F 2 2) 5 ) 5 (F 2 2) (F 2 2) F 42 C F C 5 C 5 (F 2 2) (F 2 2) 9 5 ) 5 ( 9 5 ) 5 (F 2 2) ( (F 2 2) F 2.4 C F Convert each equation from standard form to slope-intercept form. 7. 4x 1 6y x 2 5y x 1 6y 5 48 x 2 5y x 2 4x 1 6y 5 24x y 5 24x y x 1 8 y 5 2 x x 1 9y x 1 9y x 1 4x 1 9y 5 4x y 5 4x y 5 9 x 1 5 x 2 x 2 5y 5 2x y 5 2x y 5 5 x x 2 2y x 2 2y x 2 6x 2 2y 5 26x y 5 26x y 5 x x 2 8y x 2 8y x 1 x 2 8y 5 x y 5 x y 5 2 x x 1 28y x 1 28y x 2 12x 1 28y 5 212x y 5 212x y x 2 y x 2 42 Chapter Skills Practice

19 Lesson. Skills Practice page Name Date Convert each equation from slope-intercept form to standard form. 1. y 5 5x 1 8 y 5 5x x 1 y 5 5x 2 5x x 1 y y 5 24x 1 2 y 5 24x 1 2 4x 1 y 5 24x 1 4x 1 2 4x 1 y y 5 2 x 2 6 y 5 2 x 2 6 ()y 5 ( 2 x 2 6 ) y 5 2x x 1 y 5 2x 2 2x x 1 y y x 2 y x 2 (2)y 5 2 ( x 2 ) 2y 5 2x 2 6 x 1 2y 5 2x 1 x 2 6 x 1 2y y 5 25x 2 1 y 5 25x 2 1 5x 1 y 5 25x 1 5x 2 1 5x 1 y y 5 x y 5 x (4)y 5 4 ( 4 x 1 10 ) 4y 5 x x 1 4y 5 x 2 x x 1 4y 5 40 Chapter Skills Practice 4

20 Lesson. Skills Practice page 4 Solve each equation for the variable indicated. 19. The formula for the area of a triangle is A 5 1 bh. Solve the equation for h. 2 A bh (2)A 5 2 ( 1 2 bh ) 2A 5 bh 2A 5 bh b b 2A b 5 h 20. The formula for the area of a trapezoid is A (b 1 1 b 2 )h. Solve the equation for b 1. A (b 1 1 b 2 )h 2A (b 1 1 b 2 )h 2A 5 (b 1 1 b 2 )h 2A h 5 (b 1 b )h 1 2 h 2A h 5 b 1 b 1 2 2A h 2 b 5 b 1 b 2 b A h 2 b 5 b The formula for the area of a circle is A 5 pr 2. Solve the equation for r. A 5 pr 2 A p 5 pr2 A p 5 r2 A p 5 A p r 2 p 5 r 44 Chapter Skills Practice

21 Lesson. Skills Practice page 5 Name Date 22. The formula for the volume of a cylinder is V 5 pr 2 h. Solve the equation for h. V 5 pr 2 h V pr 5 h 2 pr2 pr 2 V pr 5 h 2 2. The formula for the volume of a pyramid is V 5 1 lwh. Solve the equation for w. V 5 1 lwh ()V 5 ( 1 lwh ) V 5 lwh V 5 lwh lh lh V lh 5 w 24. The formula for the volume of a sphere is V 5 4 pr. Solve the equation for r. V 5 4 pr V 5 ( 4 pr ) V 5 4pr V V V 4p 5 4pr 4p 4p 5 r 4p 5 r V 4p 5 r Chapter Skills Practice 45

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23 Lesson.4 Skills Practice Name Date A Growing Business Combining Linear Equations Problem Set Write a linear function in two different ways to represent each problem situation. 1. Mei paints and sells ceramic vases for $5 each. Each month she typically breaks vases in the kiln. Write a linear function that represents the total amount Mei earns each month selling vases taking into account the value of the vases she breaks. f(x) 5 5(x 2 ) f(x) 5 5x Isabel makes and sells fruit pies at her bakery for $12.99 each. Each month she gives away 4 pies as samples. Write a linear function that represents the total amount Isabel earns each month selling fruit pies taking into account the value of the pies she gives away as samples. f(x) (x 2 4) f(x) x Mattie sells heads of lettuce for $1.99 each from a roadside farmer s market stand. Each week she loses 2 heads of lettuce due to spoilage. Write a linear function that represents the total amount Mattie earns each week selling heads of lettuce taking into account the value of the lettuce she loses due to spoilage. f(x) (x 2 2) f(x) x Carlos prints and sells T-shirts for $14.99 each. Each month 5 T-shirts are misprinted and cannot be sold. Write a linear equation that represents the total amount Carlos earns each month selling T-shirts taking into account the value of the T-shirts that cannot be sold. f(x) (x 2 5) f(x) x Odell prints and sells posters for $20 each. Each month 1 poster is misprinted and cannot be sold. Write a linear equation that represents the total amount Odell earns each month taking into account the value of the poster that cannot be sold. f(x) 5 20(x 2 1) f(x) 5 20x 2 20 Chapter Skills Practice 47

24 Lesson.4 Skills Practice page 2 6. Emilio builds and sells homemade wooden toys for $40 each. Each month he donates toys to a children s hospital. Write a linear equation that represents the total amount Emilio earns each month selling toys taking into account the toys he donates. f(x) 5 40(x 2 ) f(x) 5 40x Write a linear function to represent each problem situation. 7. A cereal manufacturer has two production lines. Line A produces a variety of cereal that is sold for $ per box. Line A typically produces 4 boxes per day that do not meet company standards and cannot be sold. Line B produces a variety of cereal that is sold for $2 per box. Line B typically produces 6 boxes per day that do not meet company standards and cannot be sold. Line A and Line B produce the same total number of boxes each day. The linear functions a(x) 5 (x 2 4) and b(x) 5 2(x 2 6) represent the total amount each line can produce taking into account the boxes that do not meet company standards and cannot be sold. Write a linear function that represents the total number of boxes the lines can produce combined. 1 Line A: 2 x a(x) 5 ( 1 2 x 2 4 ) 1 Line B: 2 x b(x) 5 2 ( 1 2 x 2 6 ) c(x) 5 a(x) 1 b(x) 5 ( 1 2 x 2 4 ) 1 2 ( x 2 6 ) x x x The linear function c(x) 5 x 2 24 represents the total number of boxes that Line A 2 and Line B can produce combined. 48 Chapter Skills Practice

25 Lesson.4 Skills Practice page Name Date 8. A pretzel manufacturer has two production lines. Line A produces a variety of pretzel that is sold for $2.40 per bag. Line A typically produces bags per day that do not meet company standards and cannot be sold. Line B produces a variety of pretzel that is sold for $.60 per bag. Line B typically produces 4 bags per day that do not meet company standards and cannot be sold. Line A produces times as many bags as Line B each day. The linear functions a(x) 5 2.4(x 2 ) and b(x) 5.6(x 2 4) represent the total number of bags each line can produce taking into account the bags that do not meet company standards and cannot be. Write a linear function that represents the total number of bags the lines can produce combined. Line A: 4 x a(x) ( 4 x 2 ) Line B: 1 4 x b(x) 5.6 ( 1 4 x 2 4 ) c(x) 5 a(x) 1 b(x) ( 4 x 2 ) 1.6 ( 1 4 x 2 4 ) 5 1.8x x x The linear function c(x) 5 2.7x represents the total number of bags that Line A and Line B can produce combined. 9. Carlos has a roadside stand that sells peaches. He sells his peaches for $1.99 per pound. He typically loses 5 pounds per week to spoilage. Hector also has a roadside stand that sells peaches. He sells his peaches for $2.49 per pound. He typically only loses 1 pound per week to spoilage. Carlos stand sells twice as many peaches per week as Hector s stand. The linear functions c(x) (x 2 5) and h(x) (x 2 1) represent the total amount each stand can earn taking into account the peaches lost to spoilage. Write a linear function that represents the total amount that 2 Carlos and Hector can earn combined. Carlos s stand: x c(x) ( 2 x 2 5 ) Hector s stand: 1 x h(x) ( 1 x 2 1 ) f(x) 5 c(x) 1 h(x) ( 2 x 2 5 ) ( 1 x 2 1 ) 1.x x x The linear function f(x) x represents the total amount that Carlos and Hector can earn combined. Chapter Skills Practice 49

26 Lesson.4 Skills Practice page A lamp manufacturer has two production lines. Line A produces a lamp model that is sold for $24.99 each. Line A typically produces 2 lamps per day that do not meet company standards and cannot be sold. Line B produces a lamp model that is sold for $4.99 each. Line B typically produces 1 lamp per day that does not meet company standards and cannot be sold. Line A produces half as many lamps as Line B each day. The linear functions a(x) (x 2 2) and b(x) (x 2 1) represent the total number of lamps each line can produce taking into account the lamps that do not meet company standards and cannot be sold. Write a linear function that represents the total number of lamps the lines can produce 1 combined. Line A: x a(x) ( 1 x 2 2 ) Line B: 2 x b(x) ( 2 x 2 1 ) c(x) 5 a(x) 1 b(x) ( 1 x 2 2 ) ( 2 x 2 1 ) 8.x x x The linear function c(x) x represents the total number of lamps that Line A and Line B can produce combined. 11. A jean manufacturer has two production lines. Line A produces a style that is sold for $42 each. Line A typically produces 2 pairs per day that do not meet company standards and cannot be sold. Line B produces a style that can be sold for $65 each. Line B typically produces pairs per day that do not meet company standards and cannot be sold. Line A produces three times as many pairs of jeans as Line B each day. The linear functions a(x) 5 42(x 2 2) and b(x) 5 65(x 2 ) represent the total number of pairs of jeans that each line can produce taking into account the jeans that do not meet company standards and cannot be sold. Write a linear function that represents the total number of pairs of jeans the lines can produce combined. Line A: 4 x a(x) 5 42 ( 4 x 2 2 ) Line B: 1 4 x b(x) 5 65 ( 1 4 x 2 ) c(x) 5 a(x) 1 b(x) 5 42 ( 4 x 2 2 ) 1 65 ( 1 4 x 2 ) 5 1.5x x x The linear function c(x) x represents the total amount that Line A and Line B can make combined. 50 Chapter Skills Practice

27 Lesson.4 Skills Practice page 5 Name Date 12. Jada makes and sells handmade puzzles for $2 each. Each month she donates 2 puzzles to a retirement community. Ronna also makes and sells handmade puzzles for $28 each. Each month she donates 2 puzzles to a childcare center. Jada and Ronna make the same number of puzzles each month. The linear functions j(x) 5 2(x 2 2) and r(x) 5 28(x 2 2) represent the total amount each girl can earn taking into account the puzzles that are donated and not sold. Write a linear function that represents the total 1 amount Jada and Ronna can earn combined. Jada: 2 x j(x) 5 2 ( 1 2 x 2 2 ) Ronna: 1 2 x r(x) 5 28 ( 1 2 x 2 2 ) f(x) 5 j(x) 1 r(x) 5 2 ( 1 2 x 2 2 ) 1 28 ( 1 2 x 2 2 ) 5 16x x x The linear function f(x) 5 0x represents the total amount that Jada and Ronna can earn combined. Chapter Skills Practice 51

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Answers for the lesson Plot Points in a Coordinate Plane

LESSON 3.1 Answers for the lesson Plot Points in a Coordinate Plane Skill Practice 1. 5; 23 2. No; the point could lie in either Quadrant II or Quadrant IV. 3. (3, 22) 4. (, 21) 5. (4, 4) 6. (24, 3) 7.