# Answers (Anticipation Guide And Lesson 4-1) - Mrs. Speer's Site

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PERIODGraphing Equations in Slope-Intercept FormStudy Guide and Intervention (continued)Chapter 461345Years Since 19992601.0%1.5%2.0%2.5%3.0%3.5%345740Years Since 201020Glencoe Algebra 1xProjected UnitedStates PopulationSource: The World Almanac0300320340360380400P2Years Since 20011Full-length Cassette SalesSource: RIAA2. POPULATION The population of the United States isprojected to be 300 million by the year 2010. Between2010 and 2050, the population is expected to increaseby about 2.5 million per year.a. Write an equation to find the population P in any year xbetween 2010 and 2050. P 2,500,000x 300,000,000b. Graph the equation on the grid at the right.c. Find the population in 2050. about 400,000,0000255075100125Music Cassettes SoldSource: The World Almanac1. MUSIC In 2001, full-length cassettes represented 3.4% oftotal music sales. Between 2001 and 2006, the percentdecreased by about 0.5% per year.a. Write an equation to find the percent P of recorded musicsold as full-length cassettes for any year x between2001 and 2006. P -0.5x 3.4b. Graph the equation on the grid at the right.c. Find the percent of recorded music soldas full-length cassettes in 2004. 1.9%Exercisesc. Find the approximate number of music cassettessold in 2003.N -27x 124Original equationN -27(4) 124Replace x with 3.N 16Simplify.There were about 16 million music cassettes sold in 2003.b. Graph the equation.The graph of N -27x 124 is a line that passesthrough the point at (0, 124) and has a slope of -27.Number of Cassettesa. Write a linear equation to find the average number of music cassettes sold inany year after 1999.The rate of change is -27 million per year. In the first year, the number of musiccassettes sold was 124 million. Let N the number of millions of music cassettes sold.Let x the number of years after 1999. An equation is N -27x 124.ExampleMEDIA Since 1999, the number of music cassettes sold hasdecreased by an average rate of 27 million per year. There were 124 million musiccassettes sold in 1999.Modeling Real-World Data4-1DATEPercent of Total Music SalesPopulation (millions)A2Glencoe Algebra 1Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Chapter 4PERIODGraphing Equations in Slope-Intercept FormSkills PracticeDATE(0, –3)(2, 1)y 2x - 3Oyxxy(2, –4)y -3x 2O(0, 2)Oy13. y -2x - 110.xxa. Write an equation in slope-intercept form for the total cost cof buying a rental card and renting m movies. c 10 2mChapter 4 227c. Find the cost of buying a rental card and 6 movies.b. Graph the equation.O0101214161820cxx1345mGlencoe Algebra 1Movies Rented2c 10 2mVideo StoreRental CostsOyy -x - 1(0, –1)14. x y -311.15. VIDEO RENTALS A video store charges 10 for a rental cardplus 2 per rental.OyGraph each equation.12. y x 49.(2, –3)7. slope: 1, y-intercept: -12 y x - 12y8. slope: 0, y-intercept: 8 y 85. slope: 3, y-intercept: 2 y 3x 2Write an equation in slope-intercept form for each graph shown.4. slope: 7, y-intercept: 1 y 7x 16. slope: -4, y-intercept: -9 y -4x - 93. slope: -6, y-intercept: -2 y -6x - 22. slope: -2, y-intercept: 7 y -2x 71. slope: 5, y-intercept: -3 y 5x - 3Write an equation of a line in slope-intercept form with the given slopeand y-intercept.4-1NAMETotal Cost ( )NAMEAnswers (Lesson 4-1)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Lesson 4-1Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Chapter 4DATEPERIODWriting Equations in Slope-Intercept FormStudy Guide and Intervention (continued)y2 -2, y1 2, x2 3, x1 1Slope formulaA5(0, –3)(1, 1)y 4x - 3Oyx(4, 0)y -x 4Oy(0, 4)Chapter 421y - x 210. (4, 0), (0, 2)y 3x 58. (10, -1), (4, 2)7. (-2, -1), (2, 11)xGlencoe Algebra 112Answers35 y x 511. (-3, 0), (0, 5)1y - x 42y 5x 25. (0, 2), (1, 7)2.y -2x 44. (-1, 6), (7, -10)1.31 y x 1(–3, 0) O(0, 1)yx5Glencoe Algebra 18 y x 1612. (0, 16), (-10, 0)3 y x 479. (-14, -2), (7, 7)y -4x - 16. (6, -25), (-1, 3)3.Write an equation of the line that passes through each pair of points.Exercisesm -2Simplify.y mx bSlope-intercept form2 -2(1) bReplace m with -2, y with 2, and x with 1.2 -2 bMultiply.4 bAdd 2 to each side.Therefore, the equation is y -2x 4.3-1-2 - 2m 12m x2 - x1y -yExampleWrite an equation of the line that passes through (1, 2) and (3, -2).Find the slope m. To find the y-intercept, replace m with its computed value and (x, y) with(1, 2) in the slope-intercept form. Then solve for b.Write an Equation Given Two Points4-2NAMECopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.PERIODWriting Equations in Slope-Intercept FormSkills PracticeDATEOym 1(4, 1)(-1, 2)Oy 2x 4m 2yO(3, –2)yy -x 1(–2, 3)xO(1, 1)y 2x - 1(–1, –3)yx(2, –1)yy -2x 3O(0, 3)y -2x 418. (-1, 6), (3, -2)y 3x - 415. (1, -1), (3, 5)12.xy -4x - 169. (-5, 4); slope -4y 3x - 8Chapter 4 6513b. Estimate the price of a share of stock five weeks ago.p 3w 80Glencoe Algebra 1a. Write a linear equation to find the price p of a share of XYZ Corporation stock wweeks from now.19. INVESTING The price of a share of stock in XYZ Corporation was 74 two weeks ago.Seven weeks ago, the price was 59 a share.y 3x - 617. (3, 3), (1, -3)16. (-2, 4), (0, 6)y x 6y -x 514. (1, 4), (6, -1)11.y 2x 113. (1, 3), (-3, -5)10.x6. (2, -2); slope 33.Write an equation of the line that passes through each pair of points.y 2x 48. (-3, -2); slope 2y 5x - 157. (3, 0); slope 5xy -2x 10y x-3Oy5. (4, 2); slope -2x2.y 4x 5y -3x 1m –3(–1, 4)4. (1, 9); slope 41.Write an equation of the line that passes through the given point with thegiven slope.4-2NAMEAnswers (Lesson 4-2)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Lesson 4-2Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

A6Glencoe Algebra 1PERIODWriting Equations in Slope-Intercept FormPracticeDATE(1, 2)Ox722)221 3y - x (158. -2, ; slope - 2y 09. (5, 0); slope 011.O(0, 5)y(4, 1)xy22239y - x - 4411y - x Chapter 414Glencoe Algebra 120. WEATHER It is 76 F at the 6000-foot level of a mountain, and 49 F at the 12,000-footlevel of the mountain. Write a linear equation to find the temperature T at an elevationx on the mountain, where x is in thousands of feet. T -4.5x 10319. DANCE LESSONS The cost for 7 dance lessons is 82. The cost for 11 lessons is 122.Write a linear equation to find the total cost C for ℓ lessons. Then use the equation tofind the cost of 4 lessons. C 10ℓ 12; 5252 y x 118. (1, 0), (5, -1)317. (-3, 0), (1, -6)16. (0, 1), (5, 3)34 - 1y x 415. (-2, -3), (4, 5)x1 y x 1y -2x - 5(–1, –3)O(–3, 1)14. (-4, -2), (4, 0)12.2y -413. (0, -4), (5, -4)(2, –4)(4, –2)xy -x 5Oyy x-610.Write an equation of the line that passes through each pair of points.72 1y x 6 727. (3, 7); slope 237y - x - 2yy -x - 4(–1, –3)m –1O1 y x 1x3.y -3x - 11y -2x - 2m –2(–2, 2)y36. (1, -5); slope - x2.15. (4, 3); slope y 3x - 1m 3Oy4. (-5, 4); slope -31.Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Chapter 4Write an equation of the line that passes through the given point and has thegiven slope.4-2NAMEp 5441y 123,000153. CENSUS The population of Laredo,Texas, was about 215,500 in 2007. Itwas about 123,000 in 1990. If we assumethat the population growth is constantand y represents the number of yearsafter 1990, write a linear equation tofind p, Laredo’s population for any yearafter 1990.k 3000y 41,2502. JOBS Mr. Kimball receives a 3000annual salary increase on theanniversary of his hiring if he receivesa satisfactory performance review.His starting salary was 41,250. Writean equation to show k, Mr. Kimball’ssalary after y years at this companyif his performance reviews arealways satisfactory.Chapter 4DATEPERIOD5.5U.S.63.56.5457.585.568.5Glencoe Algebra 1No. It is not likely a valid datapoint because the U.K. sizingprobably does not includezero. However, the point isthe y-intercept of the linerepresented by the data ifthe data were to continueindefinitely in both directions.c. Is the y-intercept a valid data pointfor the given information?b. What is the slope and y-intercept ofthe line?Slope 1; y-intercept 2.5y x 2.5a. Write a linear equation to determineany U.S. size if you are given the U.K.size.74.5Women’s Shoe SizesSource: DanceSport UK3U.K.5. SHOE SIZES The table shows howwomen’s shoe sizes in the UnitedKingdom compare to women’s shoe sizesin the United States.y 40; slope is 0. The line ishorizontal.4. WATER Mr. Williams pays 40 a monthfor city water, no matter how manygallons of water he uses in a givenmonth. Let x represent the number ofgallons of water used per month. Let yrepresent the monthly cost of the citywater in dollars. What is the equation ofthe line that represents this information?What is the slope of the line?Writing Equations in Slope-Intercept FormWord Problem Practice1. FUNDRAISING Yvonne and her friendsheld a bake sale to benefit a shelter forhomeless people. The friends sold 22cakes on the first day and 15 cakes onthe second day of the bake sale. Theycollected 88 on the first day and 60 onthe second day. Let x represent thenumber of cakes sold and y represent theamount of money made. Find the slope ofthe line that would pass through thepoints given. 44-2NAMEAnswers (Lesson 4-2)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Lesson 4-2Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Chapter 4EnrichmentDATEPERIODA7Oyxy -20x - 532. y 3x2 4x - 5, (-4, 27)y -2x 63. y 5 - x2, (1, 4)Chapter 4Glencoe Algebra 1Answers16Glencoe Algebra 15. Find the slope of the line tangent to the curve y ax2 bx c at x by finding the slopeof the line through the points (0, c) and (2x, 4ax2 2bx c). Does this answer work forx 0 in the answer you found to problem 4? m 2ax b, yes4. Find the slope of the line tangent to the curve at x 0 for the general equationy ax2 bx c. m by x 31. y x2 - 3x 7, (2, 5)For 1–3, find the equations of the lines tangent to each curve through thegiven point.ExercisesStep 3: Now use this slope and the point (2, 12) to find the equation of the tangent line.y mx bSlope " intercept form.12 7(2) bReplace x with 2, y with 12, and m with 7.-2 bSolve for b.So, the equation of the tangent line to y x2 3x 2 through the point (2, 12) is y 7x – 2.3-1Step 2: Find the slope of the line that goes through these two points.20 - 6m or 7Step 1: Find two more points. Use x 1 and x 3.When x 1, y 12 3(1) 2 or 6.When x 3, y 32 3(3) 2 or 20.So, the two ordered pairs are (1, 6) and (3, 20).ExampleTo find the equation of a tangentline to the curve y x2 3x 2 through thepoint (2, 12), first find two points on the curvewhose x-values are equidistant from the x-valueof the point the tangent needs to go through.For quadratic functions (functions of the form ax bx c), the equation of the tangent linecan be found. This is based on the fact that the slope through any two points on the curveis equal to the slope of the line tangent to the curve at the point whose x-value is halfwaybetween the x-values of the other two points.2A tangent line is a line that intersects a curve at a point with the same rate of change, orslope, as the rate of change of the curve at that point.Tangent to a Curve4-2NAMECopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Point-Slope Form2225m - ; (x1, y1) (6, 1)Point-slope formy - y1 m(x - x1)Point-slope formy - (-1) 0(x - 4)m 0; (x1, y1) (4, -1)y 1 0Simplify.Therefore, the equation is y 1 0.Example 2Write an equation inpoint-slope form for a horizontal linethat passes through (4, -1).m 1(4, 1)xy-1 x-4OyOyy-2 0(–3, 2)m 0x443 y-9 (x 4)38. (4, 9), m y - 2 6(x 7)5. (-7, 2), m 62.(2, –3)m –2xy-3 x-821y 5 - (x 4)19. (-4, -5), m - 2y 3 -2(x - 2)Oy6. (8, 3), m 13.Chapter 4y 017Glencoe Algebra 112. Write an equation in point-slope form for a horizontal line that passes through (5, 0).11. Write an equation in point-slope form for a horizontal line that passes through(-5, 6). y - 6 010. Write an equation in point-slope form for a horizontal line that passes through(4, -2). y 2 0y-7 07. (-6, 7), m 0y - 1 4(x - 2)4. (2, 1), m 41.Write an equation in point-slope form for the line that passes through the givenpoint with the slope provided.25Therefore, the equation is y - 1 - (x - 6).y - y1 m(x - x1)5(x - 6)y - 1 - PERIODy - y1 m(x - x1), where (x1, y1) is a given point on a nonvertical lineand m is the slope of the lineExample 1Write an equation inpoint-slope form for the line that passes5through (6, 1) with a slope of - .Point-Slope FormExercisesDATEStudy Guide and InterventionPoint-Slope Form4-3NAMEAnswers (Lesson 4-2 and Lesson 4-3)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Lesson 4-3Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

A8Glencoe Algebra 1PERIODPoint-Slope FormAx By CPoint-SlopeFormStandardFormMultiply each side by 3.Original equation41x 2y - 2 - 41x 4y - 41y - 2 - (x - 8)Distributive PropertyOriginal equation335x - 3y -275(3Chapter 4y 3x 5110. y - 6 3 x - )18y -2x - 1411. y 4 -2(x 5)32Glencoe Algebra 11 - 8y x 2335112. y (x - 2)41y - x 61 y x 3y 4x - 12319. y - 8 - (x 8)1(x - 6)8. y - 5 42x 5y -187. y 4 4(x - 2)Write each equation in slope-intercept form.x y 226. y 4 - (x - 1)55. y - 4 (x 3)4. y 3 -(x - 5)32x - 3y 2423. y 2 (x - 9)x 3y 912. y - 1 - (x - 6)3x y 11. y 2 -3(x - 1)Write each equation in standard form.Exercises3y 15 2(x - 6)Distributive PropertyAdd 2 to each side.3y 15 2x - 12Distributive PropertyTherefore, the slope-intercept form of the3y 2x - 27Subtract 15 from each side.1equation is y - x 4.-2x 3y -27Add -2x to each side.42x - 3y 27Multiply each side by -1.Therefore, the standard form of the equationis 2x - 3y 27.2(x - 6)3(y 5) 3 (3)32(x - 6)y 5 1Example 2Write y - 2 - (x - 8) in4slope-intercept form.A and B are not both zero. Usually A is nonnegative and A, B, andC are integers whose greatest common factor is 1.m slope; (x1, y1) is a given point.2Example 1Write y 5 (x - 6) in3standard form.y mx by - y1 m(x - x1)Slope-InterceptFormm slope; b y-interceptStudy Guide and Intervention (continued)DATECopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Chapter 4Forms of Linear Equations4-3NAMEPoint-Slope FormSkills PracticeDATEPERIODyOxy 2 3(x 1)(–1, –2)m 3(1, –2)34 y-3 (x 3)348. (3, 3), m x 2y 82117. y - 2 - (x - 4)4x - y -1814. y - 6 4(x 3)3x y -311. y 9 -3(x - 2)3219Glencoe Algebra 1y x 11 y x 52y 3x 2324. y - 8 3(x 5)y -2x 221. y - 6 -2(x 2)x - 3y 30118. y 11 (x 3)5x y 1015. y 5 -5(x - 3)4x - y -2312. y - 7 4(x 4)41127. y - x Chapter 445y 1 - (x 5)59. (-5, -1), m - 1y - x - 432xy 3 -4(x - 1)126. y 1 - (x 9)3y 6x - 3(2, –3)y 3 0m 0yO6. (1, -3), m -43.125. y - 2 (x 6)223. y - 3 6(x - 1)y -5x 14y -x - 620. y 2 -(x 4)22. y 1 -5(x - 3)y 3x - 219. y - 4 3(x - 2)xy - 6 8(x 4)Write each equation in slope-intercept form.2x y 1616. y - 10 -2(x - 3)x y 513. y - 4 -(x - 1)x - y -110. y 1 x 2Oyy 2 -(x - 1)m –15. (-4, 6), m 82.Write each equation in standard form.y 6 x-47. (4, -6), m 1y-1 04. (3, 1), m 01.Write an equation in point-slope form for the line that passes through the givenpoint with the slope provided.4-3NAMEAnswers (Lesson 4-3)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Lesson 4-3Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

A9Point-Slope FormPracticeDATEPERIOD433(4(4)2121. y - -2 x - 3y -5x - 57y -7x - 81120. y - -3 x 418. y - 3 -5(x 12)17. y 1 -7(x 1)5x - 2y -2315. y - 4 2.5(x 3)4x - 3y -6412. y - 6 (x - 3)2x - y -39. y 7 2(x 5)1y 3 (x - 3)316. (3, -3), m y 4 03. (-3, -4), m 0Chapter 4Glencoe Algebra 120Answersc. What is the daily fee? 40b. Write the equation in slope-intercept form. y 0.5x 40Glencoe Algebra 1a. Write the point-slope form of an equation to find the total charge y for any number ofmiles x for a one-day rental. y - 64 0.5(x - 48)23. MOVING There is a set daily fee for renting a moving truck, plus a charge of 0.50 permile driven. It costs 64 to rent the truck on a day when it is driven 48 miles.c. What is the fee for the use of a trash dumpster? 60b. Write the equation in slope-intercept form. y 15x 60a. Write the point-slope form of an equation to find the total fee y for any number ofhours x. y - 195 15(x - 9)plus a one-time fee for the use of a trash dumpster. The total fee for 9 hours of serviceis 195.3 17y x 11y -3x - y -2x 22622. CONSTRUCTION A construction company charges 15 per hour for debris removal,2319. y - 5 (x 4)y 4x 616. y 2 4(x 2))12x 5y 753x - 2y 2Write each equation in slope-intercept form.14. y - 3 -2.4(x - 5)3x 4y -11311. y 2 - (x 1)x y 128. y - 10 -(x - 2)13. y 4 1.5(x 2)3x - 2y -222310. y - 5 (x 4)3x - y -57. y - 11 3(x - 2)552y - 5 - (x 8)25. (-8, 5), m - y 6 -(x - 1)2. (1, -6), m -1Write each equation in standard form.43y - 3 - (x - 1)434. (1, 3), m - y - 2 -3(x - 2)1. (2, 2), m -3Write an equation in point-slope form for the line that passes through the givenpoint with the slope provided.4-3NAMEPoint-Slope Formy5 10 15 20 25 30 35 xNumber of ChirpsChapter 4Sample answer:T - 60 1(n - 20)0102030405060703. NATURE In a near perfect linearrelationship, the frequency of a malecricket’s chirp matches the outdoortemperature. The relationship isexpressed by the equation T n 40,where T is the temperature in degreesFahrenheit and n is the number of chirpsthe cricket makes in 14 seconds. Usethe information on the graph below towrite a point-slope form of the equationfor the line.4x - y 02. GEOMETRY The perimeter of a squarevaries directly with the side length. Thepoint-slope form of the equation for thisfunction is y - 4 4(x - 1). Write theequation in standard form.d - 12 12(h - 1)21DATEPERIOD05001000 1500 2000Horizontal Distance (ft)2500x - 2y 0Glencoe Algebra 1c. Write the equation in standard form.b. Write the equation from part a inslope -intercept form. y 0.5xy - 0 0.5(x - 0)a. Write an equation in point-slope formfor the line representing the jet’shorizontal trajectory.02004006008001000120014005. AVIATION A jet plane takes off andclimbs consistently 20 feet for every 40feet it moves horizontally. The graphshows the trajectory of the jet.y - 18 3.5(x - 5)4. CANOEING Geoff paddles his canoe atan average speed of 3.5 miles per hour.After 5 hours of canoeing, Geoff hastraveled 18 miles. Write an equation inthe point-slope form to find the totaldistance y for any number of hours x.Word Problem Practice1. BICYCLING Harvey rides his bike at anaverage speed of 12 miles per hour. Inother words, he rides 12 miles in 1 hour,24 miles in 2 hours, and so on. Let h bethe number of hours he rides and d bedistance traveled. Write the equation forthe relationship between distance andtime in point-slope form.4-3NAMETemperature ( F)Chapter 4Height (ft)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Answers (Lesson 4-3)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Lesson 4-3Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

A10Glencoe Algebra 1EnrichmentPERIO

Lesson 4-1 Chapter 4 5 Glencoe Algebra 1 Study Guide and Intervention Graphing Equations in Slope-Intercept Form Slope-Intercept Form Slope-Intercept Form y mx b, where m is the given slope and b is the y-intercept Write an equation in slope-intercept form for the line with a slope of -4 and a y-intercept of 3. y The mx b Slope .

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