ALGEBRA 1 STUDENT WORKBOOK 2 TOPICS 4-6

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1 ALGEBRA 1 STUDENT WORKBOOK TOPICS -6 LINEAR EQUATIONS 5.1 Rate of Change and Slope 5. Direct Variation QUIZ Slope-Intercept Form QUIZ Point Slope Form 5.5 Standard Form QUIZ 16 QUIZ 17 SYSTEMS OF EQUATIONS 6.1 Solving a Sstem b Graphing QUIZ Solving a Sstem b Substitution QUIZ Solving a Sstem b Elimination QUIZ 0 QUIZ 1 FUNCTIONS.1 Using Graphs to Relate Two Quantities QUIZ 30. Patterns and Linear Functions QUIZ 31.6 Formalizing Relations and Functions QUIZ 3 STUDY ISLAND TOPICS PA CORE 8 Proportional Relationships Solving Linear Equations Sstems of Equations Functions Linear VS Nonlinear Linear Relationships PA KEYSTONE Rate of Change Linear Equations Write or Identif Linear Equation Sstem of Linear Equations Patters Linear Functions Name: Period 1

2 Name Class Date 5-1 Practice Form G Rate of Change and Slope Determine whether each rate of change is constant. If it is, find the rate of change and eplain what it represents Find the slope of each line Find the slope of the line that passes through each pair of points. 7. (, 1), (0, 0) 8. (, 5), (6, ) 9. (3, 8), (7, 3) 10. (1, 0), (, ) 11. (8, ), (6, 3) 1. (, 3), (6, 5) Find the slope of each line

3 Name Class Date 5-1 Practice (continued) Form G Rate of Change and Slope Without graphing, tell whether the slope of a line that models each situation is positive, negative, zero, or undefined. Then find the slope. 16. The cost of tickets to the amusement park is $19.50 for 1 ticket and $78 for tickets. 17. The late fee is $ regardless of the number of das the movie is late. 18. On the trip, Jerr had his cruise control set at 60 mi/h for hours. 19. The contract states that ever da past the agreed upon completion date the project is not finished, the price is reduced b $5. State the independent variable and the dependent variable in each situation. Then find the rate of change for each situation. 0. Shell delivered 1 newspapers after 0 minutes and 36 papers after 60 minutes. 1. Two pounds of apples cost $3.98. Si pounds cost $ An airplane ascended 3000 feet in 10 minutes and 500 feet in 15 minutes. Find the slope of the line that passes through each pair of points. 3. (5, 0), (5, 5). (, ), (1.5, 1.5) 5. (.75, 3.575), (.5, 1.5) (3.35, 6.5), (5.65, 3.5) 9. Writing Eplain wh the slope of a horizontal line is alwas zero. 30. Writing Describe how to draw a line that passes through the origin and has a slope of Each pair of points lies on a line with the given slope. Find or. 31. (7, ), (3, ); slope = 3. (5, ), (6, ); slope = (, 5), ( 3, 6); slope = 1 3. (1, 9), (, ); slope = 3

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6 -1- z Tt0z1pR Kjuntaf SS5o3fst7wLaruek HLtLcCQ.N Z pablnl3 mr7iug1hxtmsc srqecs9e1rtvfemd.m R zmwa5d0eo twbittuh7 ui9nafgiqneipt8er AlZg9e1bQrpaF b1e.a Worksheet b Kuta Software LLC Kuta Software - Infinite Algebra 1 Name Finding Slope From Two Points Find the slope of the line through each pair of points. 1) (19, 16), ( 7, 15) ) (1, 19), (, 7) Date Period 3) (, 7), ( 6, ) ) (0, 8), (9, 16) 5) (17, 13), (17, 8) 6) (19, 3), (0, 3) 7) (3, 0), ( 11, 15) 8) (19, ), ( 11, 10) 6

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8 -1- g Yj061f akqugt8aa vslosfytfwaadrre3 ULLQCH.0 j 0AellY nr8iwgghstlsd orzersiedrhvoexdt.o D jmvapddew pwoi9tdhb RIonWfuiwncijt8eD ha8lngeubbr7ag 91U.u Worksheet b Kuta Software LLC Kuta Software - Infinite Algebra 1 Name Finding Slope From an Equation Find the slope of each line. Date Period 1) = 5 5 ) = 3 1 3) = + 3 ) = 1 5) = 1 6) + = 8 7) = 9 8) + 5 = 10 9) = 10) 3 = 9 8

9 -- C qy0n18w VKIuXtnaD XSnoYfctkwGaAr6eA qllkc0.g B NAIlZlk 7rTiSgdhttsc hrlegs0er1vcejdd.a n WMAaHdLeD Jwipth MILnfCiCn3iktse0 jailpgdejbhr 7a Worksheet b Kuta Software LLC 11) 3 + = 6 1) 5 = 0 13) = 1 1) + 5 = 15 15) 10 + = 0 16) = 0 17) = 18) 15 = 5 19) 1 = + 0) 1 = 1) 0 = 5 ) = 9

10 Name Class Date 5- Practice Form G Direct Variation Determine whether each equation represents a direct variation. If it does, find the constant of variation =. 3 + = = = 5. 1 = = 0 Suppose varies directl with. Write a direct variation equation that relates and. Then find the value of when = = 10 when =. 8. = 6 when = = when = = 9.9 when = = 1.85 when = = 1 9 when = 3 3. Graph each direct variation equation. 13. = 5 1. = = An equilateral triangle is a triangle with three equal sides. The perimeter of an equilateral triangle varies directl with the length of one side. What is an equation that relates the perimeter p and length l of a side? What is the graph of the equation? 17. The amount a ou fill a tub varies directl with the amount of time t ou fill it. Suppose ou fill 5 gallons in 5 minutes. What is an equation that relates a and t? What is the graph of the equation? 10

11 Name Class Date 5- Practice (continued) Form G Direct Variation For the data in each table, tell whether varies directl with. If it does, write an equation for the direct variation Suppose varies directl with. Write and graph a direct variation equation that relates and. 1. = 6 when = 3.. = when =. 3. = when = 1. Tell whether the two quantities var directl. Eplain our reasoning.. the total number of miles run and the number of miles ou run per da when training for a race 5. Jackson s age and Dlan s age 6. a recipe that calls for cups of sugar for each cup of flour 7. Writing In a direct variation equation, describe how the slope of the graph of the line is related to the constant of variation. 8. Janine gets paid $16.75 per hour at her job. Write a direct variation equation where h represents the number of hours she works and d represents the amount of mone she earns. Graph the equation. 11

12 Name Class Date 5-3 Practice Slope-Intercept Form Form G Find the slope and -intercept of the graph of each equation. 1. = 3 5. = = 1. = = = =.5 Write an equation of a line with the given slope m and -intercept b. 10. m = 1, b = m =, b = 1. m = 5, b = m = 0.5, b = 6 1. m = 0, b = m = 1, b = Write an equation in slope-intercept form of each line Write an equation in slope-intercept form of the line that passes through the given points. 19. (3, 5) and (0, ) 0. (, 6) and (, ) 1. (1, 3) and (3, 1). (7, 5) and (3, 0) 3. (10, ) and (, ). (0, 1) and (5, 6) 5. (3, ) and (1, 6) 6. (, 3) and (3, ) 7. (, 8) and (3, 6) 1

13 Name Class Date 5-3 Practice (continued) Slope-Intercept Form Form G Graph each equation. 8. = = = = 3 3. = = 7 3. Hudson is alread 0 miles awa from home on his drive back to college. He is driving 65 mi/h. Write an equation that models the total distance d travelled after h hours. What is the graph of the equation? 35. When Phil started his new job, he owed the compan $65 for his uniforms. He is earning $13 per hour. The cost of his uniforms is withheld from his earnings. Write an equation that models the total mone he has m after h hours of work. What is the graph of the equation? Find the slope and the -intercept of the graph of each equation = = a = 0 13

14 -1-3 pa0h1ai rku7tual qshofvtiwkaarte LuL5C9. e ZAUllN Yrji7g6h3tcsa ArTeRsDeDrJv6erdn.X c MCanduer EwRigtthL LIdnjfiQniEtIeg UA0l9g6ewbJrMa m1o.8 Worksheet b Kuta Software LLC Kuta Software - Infinite Algebra 1 Name Graphing Lines Sketch the graph of each line. Date Period 1) ) 3) ) 5) 6) 1

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16 Name Class Date 5- Practice Point-Slope Form Form G Write an equation of the line in slope-intercept form through the given point and with the given slope m. 1. (, 1); m = 3. ( 3, 5); m = 3. (, 11); m= 3 Graph each equation.. (0, 3); m 3 5. = ( + 3) = ( + 1) 7. Write an equation in point-slope form for each line Write an equation in point-slope form of the line through the given points. Then write the equation in slope-intercept form. 11. (, 0), (, 1) 1. (3, ), (5, 3) 13. (5, 1), (3, ) 1 1. Open-Ended Write an equation of a line that has a slope of in each form. a. point-slope form b. slope-intercept form 16

17 Name Class Date 5- Practice (continued) Form G Point-Slope Form Model the data in each table with a linear equation in slope-intercept form. What do the slope and -intercept represent? Graph the line that passes through the given point and has the given slope m. 17. (3, ); m = (, 1), m = (, ); 1 m 0. Writing Describe what ou know about the graph of a line represented b the equation 1. Writing Describe how ou would use the point-slope form to write the equation of a line that passes through the points (1, ) and (3, 5) in slope-intercept form.. Writing Describe how linear data given in a table can help ou write an equation of a line in slope-intercept form. 3. A sign sas that 3 tickets cost $.50 and that 7 tickets cost $5.50. Write an equation in point-slope form that represents the cost of tickets. What is the graph of the equation? 17

18 Name Class Date 5-5 Practice Form G Standard Form Find the - and -intercepts of the graph of each equation =7. 3 = = 6. = = = 11 Draw a line with the given intercepts. 7. -intercept: -intercept: intercept: 3 -intercept: intercept: 6 -intercept: 8 Graph each equation using - and -intercepts = = = For each equation, tell whether its graph is a horizontal or a vertical line. 13. = 1. = = = 3 Ğ 5 Graph each equation. 17. = = 19. = 7 0. =3 18

19 Name Class Date 5-5 Practice (continued) Standard Form Form G Write each equation in standard form using integers. 1. =. = 5( 8) = 3( + 1). = = = 7 Ğ 9 (+ ) 7. You have onl nickels and dimes in our pigg bank. When ou ran the coins through a change counter, it indicated ou have 595 cents. Write and graph an equation that represents this situation. What are three combinations of nickels and dimes ou could have? For each graph, find the - and -intercepts. Then write an equation in standard form using integers Find the - and -intercepts of the line that passes through the given points. 30. (, ), (5, ) 31. (1, 1), (5, 7) 3. (3, ), (, 10) 19

20 -1- U 3J0e1bX zkmuetia STobfltGwLa5rOeH PLLJC7.a u batlcli rr1igehftmsc IrLesbeMrTvkehd5.P 0 3MGaodreI UwNi5tZhP FIunhfiNnji6tAes 7ADlWgEeobFr5a V1s.v Worksheet b Kuta Software LLC Kuta Software - Infinite Algebra 1 Name Graphing Lines Sketch the graph of each line. Date Period 1) ) 3) ) 5) 6) 0

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22 -1- t AW0O1gw YKJuHta8 jssomfft9w0aprjea blzlac.f F 1AklNlq CrDi6gOhTtzsP rr5eyseevrvpewdr.m l EM9aXdQeb iwxi6thhj lirncf3ivnaiet5em tadl1goeabfrfab 3W.W Worksheet b Kuta Software LLC Kuta Software - Infinite Algebra Name Review of Linear Equations Sketch the graph of each line. Date Period 1) ) 3) ) 5) 6)

23 -- i jj01z8 RKJuQtaaP CSjoBf3tiwRahrReP ilclzcq.f m kaslllv vrpidghot5so WrkeFsuekrfvpeBdG.1 I wmwasdjet qwsiwtah8 UIgnRfMimnoiht5e6 AHl7geeUbhreae GK.A Worksheet b Kuta Software LLC Write the standard form of the equation of each line given the slope and -intercept. 7) Slope =, -intercept = 8) Slope =, -intercept = Write the standard form of the equation of each line. 9) 10) 11) ( ) 1) ( ) 13) 1) Write the standard form of the equation of the line through the given point with the given slope. 15) through: (, ), slope = 16) through: (, ), slope = Write the standard form of the equation of the line through the given points. 17) through: (, ) and (, ) 18) through: (, ) and (, ) Write the standard form of the equation of the line described. 19) through: (, ), parallel to 0) through: (, ), parallel to 1) through: (, ), perp. to ) through: (, ), perp. to 3

24 -1-9 T00D1Cu rktumtbai pscoofxttwdavrkem hlulncz.3 p fajlnl8 FrTiGgdhct0sN trjels3ezrpvoeodf.9 h M6awdieZ Ew3iYtYhc pibn9fhienfihtpex BA5lZgIepberaD v15.b Worksheet b Kuta Software LLC Kuta Software - Infinite Algebra 1 Name Writing Linear Equations Write the slope-intercept form of the equation of each line. 1) 3 = 16 ) = 1 Date Period 3) 9 7 = 7 ) 3 = 6 5) = 15 6) = 1 7) 11 = 3 8) 11 8 = 8 Write the standard form of the equation of the line through the given point with the given slope. 9) through: (1, ), slope = 7 10) through: (3, 1), slope = 1 11) through: (, 5), slope = 1) through: (3, 5), slope = 5 3

25 -- H c9011j KXuAtUal ds9oef1tw5afrren gl8ltcp.j R FA8lPlM frri0gchutst 9rweksOetrLveefdA.U b wmpardreg VwWiAthL disnfidnistgef zaslhgiekbvrean 11B.5 Worksheet b Kuta Software LLC 13) through: (, ), slope = 1 1) through: (, 5), slope = undefined 15) through: (3, 1), slope = 1 16) through: ( 1, ), slope = Write the point-slope form of the equation of the line described. 17) through: (, ), parallel to = ) through: ( 3, 3), parallel to = ) through: (, 0), parallel to = 3 0) through: ( 1, ), parallel to = 5 + 1) through: (, 0), parallel to = ) through: (, ), parallel to = 3) through: (, ), parallel to = ) through: (, 1), parallel to = 1 1 5

26 Name Class Date 6-1 Practice Form G Solving Sstems b Graphing Solve each sstem b graphing. Check our solution = = = 11 3 = = 3 = = + 3 = = 7 = = = = = = 6 + = 3 9. = 1 + = 10. Reasoning Can there be more than one point of intersection between the graphs of two linear equations? Wh or wh not? 11. Reasoning If the graphs of the equations in a sstem of linear equations coincide with each other, what does that tell ou about the solution of the sstem? Eplain. 1. Writing Eplain the method used to graph a line using the slope and -intercept. 13. Reasoning If the ordered pair (3, ) satisfies one of the two linear equations in a sstem, how can ou tell whether the point satisfies the other equation of the sstem? Eplain. 1. Writing If the graphs of two lines in a sstem do not intersect at an point, what can ou conclude about the solution of the sstem? Wh? Eplain. 15. Reasoning Without graphing, decide whether the following sstem of linear equations has one solution, infinitel man solutions or no solution. Eplain. = = Five ears from now, a father s age will be three times his son s age, and 5 ears ago, he was seven times as old as his son was. What are their present ages? 6

27 Name Class Date 6-1 Practice (continued) Form G Solving Sstems b Graphing 17. The denominator of a fraction is greater than its numerator b 9. If 7 is subtracted from both its numerator and denominator, the new fraction equals. What is the original fraction? The sum of the distances two hikers walked is 53 mi, and the difference is 5 mi. What are the distances? 19. The result of dividing a two-digit number b the number with its digits reversed is 7 If the sum of the digits is 1, what is the number? Solve each sstem b graphing. Tell whether the sstem has one solution, infinitel man solutions, or no solution = = = 3 = = 7 = = = 1. + = = 5. = = = = = 1 = = = = 1 + = = 1 = = 5 + =1 3. The measure of one of the angles of a triangle is 35. The sum of the measures of the other two angles is 15 and the difference between their measures is 15. What are the measures of the unknown angles? 7

28 -1- i MJ0G1w8 HKFuitVau 5SRoqfItRw0ahrXe8 5L0L7CX.k s KAClslM 9rViVgzhntGsP rrpepsqeurxvceod0.z l jm5adpe vwfistohn ISn0fZi0nhi0trev ralltgcexbjrhan 71X.I Worksheet b Kuta Software LLC Kuta Software - Infinite Algebra 1 Name Solving Sstems of Equations b Graphing Solve each sstem b graphing. Date Period 1) ) 3) ) 8

29 -- Rj0107 TKXuCtaaH escofttowmaqrie MLNLmCI.U ALlTlR nrqihgghjt6sw RrCeZshevrbvNeedv.p 0 kmwahdae bwbiutth IInSfDi1nKinteq jael9g6ebyr8aw X1p.i Worksheet b Kuta Software LLC 5) 6) 7) 8) 9

30 Name Class Date 6- Practice Form G Solving Sstems Using Substitution Solve each sstem b substitution. Check our solution. 1. =. = + 3. = 10 + = 3 = 3 = 8. = = = 13 = 7 = = = = = 69 = Writing How do ou know that substitution gives the answer to a sstem of equations? Eplain. 11. Reasoning With the substitution method, which variable should ou solve for first? Eplain. 1. Writing How can ou use substitution method to solve a sstem of equations that does not have a variable with a coefficient of 1 or 1? 13. Writing When solving the sstem of equations 6 3 using 8 substitution, which variable will ou solve for and which equation will ou use to substitute into? 1. Reasoning Can ou tell that there is no solution for a sstem b just looking at the equations? Eplain and give an eample. 15. If the difference in the side lengths of two squares is 10, and the sum of the side lengths is 18, what are the side lengths? 16. A shopper purchased 8 T-Shirts and 5 pairs pants for $0. The net da, he purchased 5 T-shirts and 1 pair of pants for $11. How much does each T-shirt and each pair of pants cost? 30

31 Name Class Date 6- Practice (continued) Solving Sstems Using Substitution Form G 17. A student bought 1 bo of craons and 5 reams of paper for $5. She bought 5 boes of craons and 3 reams of paper for $50. What is the cost of each bo of craons and each ream of paper? 18. Suppose ou got 8 mangoes and 3 apples for $18 and 3 mangoes and 5 apples for $1.50. How much does each mango and each apple cost? 19. A shopper purchased tables and chairs for $00 and tables and 7 chairs for $00. What is the cost of each table and each chair? 0. If the length of the rectangle is twice the width, and the perimeter of the rectangle is 30 cm, what is length and width of the rectangle? 1. The population of a cit is,500. If the number of males is 0 more than the number of females, how man males and females are there in the cit? Solve each sstem b substitution. Tell whether the sstem has one solution, infinitel man solutions, or no solution = = = = 5 = = 0 6. = = = = = 9 9. = = = = 10 = = = = 5 9 = = 0 = 5 31

32 -1- P 80S1iG GKquhtlaY oswo1fwtzwgalruen SLCLWCr.J a CAVlolr GrUiqg9hetDsg OrewsdegrGvkeDdz.J H OMlaAdkeT LwqiUtphO eignffpiyn0i5tzex AvlQgRebIrSaR f1w. Worksheet b Kuta Software LLC Kuta Software - Infinite Algebra 1 Name Solving Sstems of Equations b Substitution Solve each sstem b substitution. Date Period 1) = = 7 ) 3 = 1 = 1 3) = = 3 ) 3 3 = 3 = ) = 3 = 18 6) = = 1 7) + = 6 5 = 1 8) 7 = 13 = 11 9) 5 + = = 1 10) 5 + = = 3

33 -- 5 Tt0G1hs AKGuqtbak FSDoafRtuwaalrKeR vl0lucq.e n haol8lw NrkiJgVhPtsb VrDes8e9rYveFdS.e d jmandjew rwqi9tthu ji9n9fpilncitaez GAulCgpeRbFrdae g1n.d Worksheet b Kuta Software LLC 11) + 3 = = 15 1) 3 8 = = 19 13) = + = 3 1) = = 13 15) = = 13 16) + = = 1 17) 3 = = 3 18) + 6 = = 5 19) 5 8 = 17 7 = 17 0) = 9 5 = 18 33

34 Name Class Date 6-3 Practice Solving Sstems Using Elimination Form G Solve each sstem using elimination =. + = 3 3. = = = 6 3 =. = 5. 3 = = + = = 5 + = 7. 3 = 8 8. = 3 9. = 6 = 5 3 = = Writing For the sstem 3 5 9, which variable should ou eliminate 3 first and wh? How will ou eliminate that variable? 11. Open-Ended If ou do not have equal coefficients for both variables, can ou still use the elimination method? Eplain. 1. In a class, 5 students take the SAT eam. The number of bos is 8 more than the number of girls. a. Write a sstem that models the above situation. b. Do ou need to multipl an of the equations b a constant? If so, which equation and what is the constant? 13. Open-Ended Write a sstem for which using the elimination method to solve the sstem is easier than the substitution method. Eplain. 1. Error Analsis A student solved a sstem of linear equations using the elimination method as follows. Describe and correct the error made b the student Multipl equation 1 b. Multipl equation b 3. Add the equations. Divide b 7. 3

35 Name Class Date 6-3 Practice (continued) Solving Sstems Using Elimination Form G 15. A farm raises a total of 0 chickens and pigs. The number of legs of the stock in the farm totals 50. How man chickens and pigs are at the farm? 16. You drive a car that runs on ethanol and gas. You have a 0-gallon tank to fill and ou can bu fuel that is either 5 percent ethanol or 85 percent ethanol. How much of each tpe of fuel should ou bu to fill our tank so that it is 50 percent ethanol? 17. Your math test has 38 questions and is worth 00 points. The test consists of multiple-choice questions worth points each and open-ended questions worth 0 points each. How man of each tpe of question are there? 18. A student bought 3 boes of pencils and boes of pens for $6. He then bought boes of pencils and boes of pens for $8. Find the cost of each bo of pencils and each bo of pens. Solve each sstem using elimination. Tell whether the sstem has one solution, infinitel man solutions, or no solution = = 1. + = 6 = = = = = 5. 3 = 3 = = = = 6. + = 7. 3 = = = 6 = = = = 0 3 = 8 + = 10 + = How is the multiplication or division propert of equalit used in the elimination method? Are the properties alwas needed? Eplain. 35

36 -1- C NE0m1eC fkfuptmah GSWozfTtTwuaAr see nlylcn.w J Aol1lC rfiqg3httss3 fr1edsefr1v5e8dj.y j QMSaedReH wxiqtth NI1nPfBi7nLiutUe ZAdl3gLeibMr sac 61b. Worksheet b Kuta Software LLC Kuta Software - Infinite Algebra 1 Name Solving Sstems of Equations b Elimination Solve each sstem b elimination. Date Period 1) = = ) + 8 = 0 + = 30 3) = 11 + = 19 ) = = 10 5) 9 = 5 9 = 3 6) 8 + = = 5 7) = = 1 8) 7 + = 8 + = 30 9) 5 + = = 18 10) + 9 = 9 3 = 6 11) = = 16 1) 7 + = = 19 36

37 -- T jf0k1uh LKgumtbaE HSSoafNtWw8areW cl6lecm.x A gaplcls trgiogzhztnsa Wr1eAsMeKrJvlevdF.3 X YMLaadoen LwKisthd eigncf6ihnhiutwe1 rablygkeabcroaw 91I.5 Worksheet b Kuta Software LLC 13) = = 6 1) = 6 7 = 10 15) 15 = = 13 16) 7 = 1 1 = 8 17) 7 8 = = 18) 5 + = = 18 19) = = 5 0) 3 = 5 5 = 10 1) 5 + = = 6 ) + 8 = = 15 3) 1 = = ) 3 + = = 10 37

38 -1-3 Rz0F1vf lkzuhtlaq oslocfxthwasr de0 YLpLBCN.H r vallxlp riivgihntdsn vr8elsreorcv5eqde.b A 7M5aadHeB gwxirtuhn VIInfkirnIijtSeV eag lg8ehberda8 gd.q Worksheet b Kuta Software LLC Kuta Software - Infinite Algebra Name Sstems of Two Equations Solve each sstem b graphing. Date Period 1) = 3 + = 3 ) = + = ) = 3 7 = 3 ) + = = Solve each sstem b substitution. 5) = 9 = 3 6) + = 10 = 13 7) = = 0 8) + 7 = 0 8 = 38

39 -- m up0p1jh mkzuatoav SuotfjtuwkaZrjeb tl6lwcb.k Y CAPlSlt mrdirghrtwsk 1rjecsrenr OvqeJdG.W v 7MXadjeC 9wlitbhM SIXnTfYiYnZi0tme kaolvgleeb1r0a3 DS.c Worksheet b Kuta Software LLC 9) = = 5 10) 7 + = = 0 11) 7 + = 19 + = 1 13) 7 + = = 0 1) 3 5 = 17 = 7 1) = 0 = 10 Solve each sstem b elimination. 15) 8 6 = = 30 16) 6 1 = 6 = 17) 8 10 = = 18) 8 = = ) 11 = 36 0 = ) = 11 = ) 0 = = 18 ) 16 = = 15 3) = 0 36 = 18 ) = = Critical thinking questions: 5) Write a sstem of equations with the solution (, 3). 39

40 -1- u RF0S1gX 9Kiuat6a6 zsvolfttewgatrxel LsLAC8.E g JATlXlk OrJiZg3hutWs GrSezsGecrvQedO.6 lmeardgea bwsi8tbhe FImnafAi8n8iatPeb za8lwgteobsrhar t1a.e Worksheet b Kuta Software LLC Kuta Software - Infinite Algebra 1 Name Sstems of Equations Word Problems 1) Find the value of two numbers if their sum is 1 and their difference is. Date Period ) The difference of two numbers is 3. Their sum is 13. Find the numbers. 3) Fling to Kampala with a tailwind a plane averaged 158 km/h. On the return trip the plane onl averaged 11 km/h while fling back into the same wind. Find the speed of the wind and the speed of the plane in still air. ) The school that Stefan goes to is selling tickets to a choral performance. On the first da of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $5 on the second da b selling 3 senior citizen tickets and child tickets. Find the price of a senior citizen ticket and the price of a child ticket. 5) The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number b 9. What is the number? 6) A boat traveled 10 miles downstream and back. The trip downstream took 10 hours. The trip back took 70 hours. What is the speed of the boat in still water? What is the speed of the current? 0

41 -- j TM0h1Gc OKlu7tAa gsgoufstywaaqreb NLaLUCh.q v WAjlXln KrliSgeh0tosA BrYeGsbeprEvaeid.N 3 qmdagdjev WwXiEtZh8 5IVnMffihnni1tAeX HA1lOgNembLr7aB B1X.H Worksheet b Kuta Software LLC 7) The state fair is a popular field trip destination. This ear the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans and 8 buses with 0 students. High School B rented and filled vans and 1 bus with 5 students. Ever van had the same number of students in it as did the buses. Find the number of students in each van and in each bus. 8) The senior classes at High School A and High School B planned separate trips to New York Cit. The senior class at High School A rented and filled 1 van and 6 buses with 37 students. High School B rented and filled vans and 1 buses with 780 students. Each van and each bus carried the same number of students. How man students can a van carr? How man students can a bus carr? 9) Brenda's school is selling tickets to a spring musical. On the first da of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second da b selling 8 senior citizen tickets and 5 child tickets. What is the price each of one senior citizen ticket and one child ticket? 10) Matt and Ming are selling fruit for a school fundraiser. Customers can bu small boes of oranges and large boes of oranges. Matt sold 3 small boes of oranges and 1 large boes of oranges for a total of $03. Ming sold 11 small boes of oranges and 11 large boes of oranges for a total of $0. Find the cost each of one small bo of oranges and one large bo of oranges. 11) A boat traveled 336 miles downstream and back. The trip downstream took 1 hours. The trip back took 1 hours. What is the speed of the boat in still water? What is the speed of the current? 1

42 Name Class Date -1 Practice Using Graphs to Relate Two Quantities Form G What are the variables in each graph? Describe how the variables are related at various points on the graph Match each graph with its related table. Eplain our answers A. B. C.

43 Name Class Date -1 Practice (continued) Using Graphs to Relate Two Quantities Form G Sketch a graph to represent the situation. Label each section. 7. You bu two shirts. The third one is free. 8. You warm up for gm class, pla basketball, and then cool down. 9. The temperature warms up during the da and then decreases at night. 10. Error Analsis DVDs cost $19.99 each for the first purchased. After that, the cost $5.99 each. Describe and correct the error in sketching a graph to represent the relationship between the total cost and the number of DVDs purchased. 11. Sketch a graph of each situation. Are the graphs the same? Eplain. a. our distance from school as ou leave our house and walk to school b. our distance from school as ou leave school and walk to our house 3

44 Name Class Date - Practice Form G Patterns and Linear Functions For each diagram, find the relationship between the number of shapes and the perimeter of the figure the form. Represent this relationship using a table, words, an equation, and a graph. 1.. For each table, determine whether the relationship is a function. Then represent the relationship using words, an equation, and a graph. 3..

45 Name Class Date - Practice (continued) Form G Patterns and Linear Functions For each table, determine whether the relationship is a function. Then represent the relationship using words, an equation, and a graph Reasoning Graph the set of ordered pairs (0, ), (1, ), (, 6), (3, 8). Determine whether the relationship is a linear function. Eplain how ou know. 8. You can make a bubble solution b miing 1 cup of liquid soap with cups of water. Represent the relationship between the cups of liquid soap and the cups of bubble solution made using a table, an equation, and a graph. Is the amount of bubble solution made a function of the amount of liquid soap used? Eplain. 5

46 Name Class Date -3 Practice Patterns and Nonlinear Functions Form G 1. A student s earnings E, in dollars, is a function of the number h of hours worked. Graph the function shown b the table. Tell whether the function is linear or nonlinear. Graph the function shown b each table. Tell whether the function is linear or nonlinear

47 Name Class Date -3 Practice (continued) Patterns and Nonlinear Functions Form G Each set of ordered pairs represents a function. Write a rule that represents the function.. (0, 1), (1, 3), (, 9), (3, 7), (, 81) 5. (0, 0), (1, 1), (, ), (3, 9), (, 16) 6. (0, 1), (1, 0.5), (, 0.5), (3, 0.15), (, 0.065) 7. (0, 0), (1, 1), (, 8), (3, 7), (, 6) 8. Reasoning A certain function fits the following description: As the value of increases b 1 each time, the value of decreases b the square of. Is this function linear or nonlinear? Eplain our reasoning. 9. Writing The rule C = 6.3r gives the approimate circumference C of a circle as a function of its radius r. Identif the independent and dependent variables in this relationship. Eplain our reasoning. 10. Open-Ended What is a rule for the function represented b (0, ), (1, 1), (, ), (3, 7)? Eplain our reasoning. 11. A landscape architect wants to make a triangular garden inside a square of land as shown at the right. What is a rule for the area A of the garden as a function of s? 7

48 Name Class Date - Practice Graphing a Function Rule Form G Graph each function rule. 1. = =3+1 Graph each function rule. Tell whether the graph is continuous or discrete.. The cost C, in dollars, for a health club membership depends on the number m of whole months ou join. This situation is represented b the function rule C = 9 + 0m. 5. The cost C, in dollars, for bananas depends on the weight w, in pounds, of the bananas. This situation is represented b the function rule C = 0.5w. 8

49 Name Class Date - Practice (continued) Graphing a Function Rule Form G Graph each function rule. 6. = = 3 8. = 9. = = 11. = Open-Ended Sketch a graph of a quadratic function that has -intercepts at 0 and. 13. Writing Describe the general shape of the graphs of functions of the form = a 3. 9

50 Name Class Date -5 Practice Form G Writing a Function Rule Write a function rule that represents each sentence less than one fourth of is.. 7 more than the quotient of a number n and is P is 9 more than half of q.. 8 more than 5 times a number is more than the quotient of a and is b. For Eercises 6 10, write a function rule that represents each situation. 6. The price p of an ice cream is $3.95 plus $0.85 for each topping t on the ice cream. 7. A babsitter s earnings e are a function of the number of hours n worked at a rate of $7.5 per hour. 8. The price p of a club s membership is $30 for an enrollment fee and $1 per week w to be a member. 9. A plumber s fees f are $75 for a house call and $60 per hour h for each hour worked. 10. A hot dog d costs $1 more than one-half the cost of a hamburger h. 11. José is 3 ears ounger than 3 times his brother s age. Write a rule that represents José s age j as a function of his brother s age b. How old is José if his brother is 5? 1. A taicab charges $.5 for the first mile and $1.50 for each additional mile. Write a rule for describing the total rate r as a function of the total miles m. What is the tai rate for 1 miles? 50

51 Name Class Date -5 Practice (continued) Writing a Function Rule Form G 13. Write a function rule for the area of a rectangle whose length is in. more than its width. What is the area of the rectangle when its width is 8 in.? 1. Write a function rule for the area of a rectangle with a length 3 ft more than two times its width. What is the area of the rectangle when its width is ft? 15. Write a function rule for the area of a triangle with a base m less than times its height. What is the area of the triangle when its height is 8 m? 16. Reasoning Write a rule that is an eample of a nonlinear function that fits the following description. When b is 9, a is 7, and a is a function of b. 17. Open-Ended Describe a real-world situation that represents a nonlinear function. 18. Writing Eplain whether or not the relationship between inches and feet represents a function. 19. Multiple Representations Use the table shown at the right. a. Graph the ordered pairs on a coordinate plane. b. Write an equation that can be used to find for an value. c. Is the equation a function? Eplain. 51

52 Name Class Date -6 Practice Form G Formalizing Relations and Functions Identif the domain and range of each relation. Use a mapping diagram to determine whether the relation is a function. 1. {(3, 6), (5, 7), (7, 7) (8, 9)}. {(0, 0.), (1, 0.8), (, 1.), (3, 1.6)} 3. { (5, ), (3, 5), (, 3), (6, )}. {(0.3, 0.6), (0., 0.8), (0.3, 0.7), (0.5, 0.5)} Use the vertical line test to determine whether the relation is a function The function w() = 60 represents the number of words w() ou can tpe in minutes. How man words can ou tpe in 9 minutes? 8. Sound travels about 33 meters per second. The function d(t) = 33t gives the distance d(t) in meters that sound travels in t seconds. How far does sound travel in 8 seconds? 5

53 Name Class Date -6 Practice (continued) Form G Formalizing Relations and Functions Find the range of each function for the given domain. 9. f () = 3 + ; {, 1, 0, 1, } 10. f () = 3 ; { 1, 0.5, 0, 0.5, 1} 11. f () = + 1; {,, 0,, } f ( ) ;{0,,,,1} Find a reasonable domain and range for each function. Then graph the function. 13. A high school is having a pancake breakfast fundraiser. The have 3 packages of pancake mi that each feed 90 people. The function N(p) = 90p represents the number of people N(p) that p packages of pancake mi feed. 1. A charter boat travels at a maimum rate of 5 miles per hour. The function d() = 5 represents the distance d(), in miles, that the boat can travel in hours. The charter boat travels a maimum distance of 75 miles from the shore. 15. Reasoning If f () = 3 and f (a) = 6, what is the value of a? Eplain. 16. Open-Ended What is a value of that makes the relation {(, ), (3, 6), (8, )} a function? 53

54 Worksheet O O 5

55 For g = { ( -5, ), ( -, -1), ( 3, -8 ), ( -, 0 ), (, -9 ) } find the indicated value a) g( - ) = b) g( ) = c) g( 3) = d) g( -5) = 55

56 O O 56

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67 Functions & Relations (c) Determine the domain, range, dependent variable and independent variable. Guided Practice Worksheet Eploring Functions & Relations 1. The refreshment stand at the amusement park sells lemonade according to the following price structure: Drink Size (oz) Price ($) (d) Based on the information given, can ou determine the price of a 6-ounce cup of lemonade? Eplain our answer. (a) Construct a mapping diagram that illustrates the connection between the drink size and price. (b) Make a graph that illustrates the connection between the drink size (-ais) and price (-ais) Librar Video Compan. All rights reserved.

68 Functions & Relations Guided Practice Worksheet 3. Eamine the table below, which shows the estimated wait time, in minutes, for riding an amusement park roller coaster at various times throughout the da. (a) Determine whether or not the relation is a function. Eplain our answer. Eploring Functions & Relations (cont d.). Eamine the mapping diagram below, which shows the price of various food items at an amusement park refreshment stand. Determine whether or not the mapping diagram represents a function. Eplain our answer. (b) Is this relation a function if the domain and range are reversed? Eplain our answer. Price Food 1 oz drink $.99 $1.19 $1.9 $ oz drink 3 oz bo of popcorn oz drink 8 oz drink oz pretzel Time of Da Estimated Wait Time (minutes) 10 am 5 11 am 10 1 pm 15 1 pm 35 pm 5 3 pm 5 pm 35 5 pm 0 6 pm 15 7 pm 10 8 pm 15 9 pm 0 10 pm 5 11 pm Librar Video Compan. All rights reserved.

69 Functions & Relations. Use the vertical line test to determine whether or not the graph from Question #1 represents a function. Eplain our answer. Guided Practice Worksheet Appling the Vertical Line Test The data in the table below shows a rider s height above the ground, in feet, during the first 60 seconds of a 10-second Ferris wheel ride. Time (seconds) Height Above Ground (feet) Make a graph of the time on the ride (-ais) versus the rider s height above ground (-ais) during the first 60 seconds of the Ferris wheel ride. 1. Make a graph of the rider s height above ground (-ais) versus the time on the ride (-ais) during the first 60 seconds of the Ferris wheel ride.. Use the vertical line test to determine whether or not the graph from Question #3 represents a function. Eplain our answer Librar Video Compan. All rights reserved.

70 Functions & Relations. Eamine the graph below, which shows the speed of a roller coaster car during the course of a ride. Determine whether or not the graph represents a function. Eplain our answer. Guided Practice Worksheet Roller Coaster Speed Is It a Function? 1. Eamine each set of ordered pairs. Construct a mapping diagram that illustrates the connection between each domain and range. Determine whether or not each set represents a function. Eplain our answer. (a) (,3) (,-) (,-) (6,5) Time (b) (,3) (,-) (3,-) (6,5) 3. Eamine the graph below, which shows the number of points earned in an arcade pinball game and the game level. Determine whether or not the graph represents a function. Eplain our answer. Pinball Game Scoring Sstem Points Librar Video Compan. All rights reserved.

71 Slope and Rate of Change Quiz 1 Multiple Choice Identif the choice that best completes the statement or answers the question. The rate of change is constant in each table. Find the rate of change. Eplain what the rate of change means for the situation. 1. The table shows the cost of a ski rental package for a given number of people. People Cost ($) a. b. c. d. dollars per person; the cost is $50 for each person. dollars per person; the cost is $00 for each person. dollars per room; the cost is $50 for each person. dollars per person; the cost is $1 for 350 people. Find the slope of the line a. 3 b. 1 c. 3 d a. b. c d. 3

72 What is the slope of the line that passes through the pair of points?. ( 8.9, 8.6), ( 3.9, 11.) a. b. 0.5 c. d (, ), (, ) a. b. c. d Short Answer The rate of change is constant in each table. Find the rate of change. Eplain what the rate of change means for the situation. 1. The table shows the number of miles driven over time. Time (hours) Distance (miles) What is the slope of the line that passes through the pair of points?. (, 8), (10, ) What is the slope of the line?

73 Graphs of Linear Equations Quiz 15 Multiple Choice Identif the choice that best completes the statement or answers the question. Graph the equation. 1. = a. c b. d

74 Balance ($) Balance ($) Balance ($) Balance ($). Giselle pas $00 in advance on her account at the athletic club. Each time she uses the club, $10 is deducted from the account. Model the situation with a linear function and a graph. a. 30 b Athletic Club Account c. 00 b Athletic Club Account b. b = b Number of Visits Athletic Club Account d. b = b Number of Visits Athletic Club Account b = Number of Visits b = Number of Visits 7

75 = 0.9( ) a. c b. d = 8 a. c b. d

76 = 0.1 a. c b. d Graph the equation. 6. = Graph the equation =

77 8. = = ( 3) Standard Form Quiz 16 Multiple Choice What are the slope and -intercept of the graph of the given equation? 7 1. = 1 a. 7 The slope is and the -intercept is 1. b. 1 7 The slope is and the -intercept is.. = a. The slope is 7.5 and the -intercept is 1.5. b. The slope is 7.5 and the -intercept is = 7 a. The slope is 7 and the -intercept is. b. The slope is 7 and the -intercept is. c. 1 The slope is and the -intercept is. 7 d. The slope is 1 7 and the -intercept is. c. The slope is 1.5 and the -intercept is 7.5. d. The slope is 1.5 and the -intercept is 7.5. c. The slope is and the -intercept is 7. d. The slope is and the -intercept is 7. Write an equation of a line with the given slope and -intercept.. m =, b = 1 5 a. c. = = b. d. = 5 = m = 3.9, b = 8.8 a. = c. = b. = d. = m = 3, b = a. = + 3 c. = 3 77 b. = 3 + d. = 3 +

78 What equation in slope intercept form represents the line that passes through the two points? 7. ( 3, ), ( 5 7, ) a. c. = = b. d. = = (5.8, 7.7), (7.8,.3) a. = c. = b. = d. = (, 6), (10, 1) a. 5 c. = = b. d. = 8 = Find the - and -intercept of the line = 7 a. -intercept is 1; -intercept is 8 c. -intercept is 6; -intercept is 9 b. -intercept is 9; -intercept is 6 d. -intercept is 8; -intercept is = 6 a. c. -intercept is 6; -intercept is 1 1 -intercept is 6; -intercept is 5 5 b. 1 d. 1 -intercept is ; -intercept is 6 -intercept is 6; -intercept is Write = + 11 in standard form using integers. 8 a. + 8 = 11 c. + 8 = 88 b. 8 = 88 d. 8 = Write = in standard form using integers. a. 10 = 3 c = 3 b = 3 d. 10 = 3 1. A paint store sells eterior paint for $3.00 a gallon and paint rollers for $5.50 each. Write an equation in standard form for the number of gallons p of paint and rollers r that a customer could bu with $15. a. 3p + 5.5r = 15 c. 3p = 5.5r + 15 b. 3r + 5.5p = 15 d = p 15. The video store rents DVDs for $5.00 each and video games for $.5 each. Write an equation in standard form for the number of DVDs d and video games g that a customer could rent with $16. a = d c. 5d +.5g = 16 b. 5g +.5d = 16 d. 5d =.5g

79 interpret Linear Functions Quiz 17 Write the slope-intercept form of the equation for the line a. b. = = 5 1 c. d. 5 = = a. b. = = c. d. 7 5 = =

80 Graph the equation. 3. = ( ) a. c b. d What is an equation of the line? a. + 3 = ( + ) c. + 3 = ( ) b. 3 = ( ) d. + 5 = ( + ) 80

81 a. = 3( + ) c. = ( + ) b. d. 5 = ( + ) = 1 3 ( + ) 3 6. The table shows the height of a plant as it grows. What equation in point-slope form gives the plant s height at an time? Let stand for the height of the plant in cm and let stand for the time in months. Time (months) Plant Height (cm) a. 5 c = ( 3) 3 = ( 15) b. 15 = 5( 3) d. The relationship cannot be modeled. 7. The table shows the height above the ground of a helicopter taking off from the top of a building. What equation in point-slope form gives the helicopter s height at an time? Let stand for the height of the helicopter in m and let stand for the time in seconds. Time (s) Height (m) a. = 8( 3) c. = ( 3) b. 3 = ( ) d. The relationship cannot be modeled. 81

82 8. = 8 a. c b. d = 0.1 a. c b. d

83 Graphing Sstems of Equations Quiz = 3 + = 3 a. c. O ( 1, 1) O ( 0.,.6) b. d. O (1, 1) (1, 0) O. = + = 3 a. c. ( 1.67, 3.68) (0.,.8) b. d. (, 1) (1, ) 83

84 What is the solution of the sstem? Use a graph. 3. = = 3 3 a. c. b. no solutions d. infinitel man solutions (0, 3) (0, 3) (0, 3) (0, 3). + 3 = =

85 = + = Sstems of Equations b Substitution Quiz = + 3 = 5 a. ( 15, 3) b. ( 3, 15) c. (3, 15) d. (0.3, 1.7). 3 + = 7 = a. (6, 3) b. (6, 7) c. d. (5, ) 3. 3 = + = + 9 a. (3, 6) b. (0, ) c. (10, 1) d. ( 1, 8). a. (1, 10) b. (6, 1) c. ( 1, ) d. ( 1, 6) 85

86 5. a. (1, ) b. (5, 1) c. (1, ) d. (, 1) 6. a. (1, 7) b. (3, 9) c. d. (, 11) Sstems of Equations b Elimination Quiz 0 1. = 8 + = 1 a. ( 1, 1) b. (1, 5) c. ( 3, 1) d. (0, ). + 5 = 16 5 = a. (, 3) b. (,.) c. (5, ) d. ( 3, ) 3. a. (90, 3) b. (3, 90) c. ( 90, 3) d. ( 3, 90). 3 = = 9 a. (3, 9) b. ( 7, 9) c. ( 3, 6) d. ( 9, 9) 5. + = = 3 a. ( 5, ) b. (, 5) c. (, 3) d. (, 1) 6. = = 18 + a. (, 1) b. ( 3, ) c. (1, 3) d. ( 3, 1) = = 38 a. (, 6) b. (5, ) c. (, 5) d. (3, 3) = 19 5 = 13 a. ( 5, 7) b. ( 1, ) c. (, 1) d. (1, ) = = 0.1 a. (1, ) b. ( 5, 37) c. (, 1) d. ( 0.1,.8) 86

87 Interpret Sstems of Equations Quiz 1 1. Tom has a collection of 1 CDs and Nita has a collection of 1 CDs. Tom is adding 3 CDs a month to his collection while Nita is adding CDs a month to her collection. Find the number of months after which the will have the same number of CDs. a. months c. 1 month b. months d. 7 months. The length of a rectangle is 3 centimeters more than 3 times the width. If the perimeter of the rectangle is 6 centimeters, find the dimensions of the rectangle. a. length = 5 cm; width = 18 cm c. length = 13 cm; width = 8 cm b. length = 13 cm; width = 5 cm d. length = 18 cm; width = 5 cm 3. A corner store sells two kinds of baked goods: cakes and pies. A cake costs $10 and a pie costs $11. In one da, the store sold 9 baked goods for a total of $9. How man cakes did the sell? a. 6 cakes c. 7 cakes b. cakes d. cakes. Sharon has some one-dollar bills and some five-dollar bills. She has 1 bills. The value of the bills is $30. Solve a sstem of equations using elimination to find how man of each kind of bill she has. a. five-dollar bills, 10 one-dollar bills c. 5 five-dollar bills, 5 one-dollar bills b. 3 five-dollar bills, 15 one-dollar bills d. 5 five-dollar bills, 9 one-dollar bills 5. The school cafeteria sells two kinds of wraps: vegetarian and chicken. The vegetarian wrap costs $1.00 and the chicken wrap costs $3.0. Toda the made $ from the 106 wraps sold. How man of the wraps sold were vegetarian? a. 80 wraps c. 67 wraps b. 39 wraps d. 8 wraps 6. Mike and Kim invest $18,000 in equipment to print earbooks for schools. Each earbook costs $6 to print and sells for $18. How man earbooks must the sell before their business breaks even? a. 1,750 earbooks b earbooks c. 1,500 earbooks d. 1,000 earbooks 7. At the local ballpark, the team charges $ for each ticket and epects to make $1,100 in concessions. The team must pa its plaers $1,500 and pa all other workers $1,700. Each fan gets a free bat that costs the team $ per bat. How man tickets must be sold to break even? a tickets b. 55 tickets c. 150 tickets d. 350 tickets 8. The local zoo is filling two water tanks for the elephant ehibit. One water tank contains 6 gal of water and is filled at a constant rate of 9 gal/h. The second water tank contains 16 gal of water and is filled at a constant rate of gal/h. When will the two tanks have the same amount of water? Eplain. Let = the number of hours the tanks are filling and let = the number of gallons in the tank. a. In hours, because the solution to the sstem is (,8). b. The will never have the same amount of water because the solution to the sstem is (,8). It is not possible to have time be hours. c. In hours, because the solution to the sstem is (,8). d. The will never have the same amount of water because the solution to the sstem is (,8). It is not possible to have gallons in the tanks. 9. Kendra owns a restaurant. She charges $3.00 for eggs and one piece of toast, and $1.80 for one egg and one piece of toast. How much does Kendra charge for an egg? A piece of toast? 10. The local zoo has two water tanks for the elephant ehibit that are leaking One water tank contains 15 gal of water and is leaking at a constant rate of gal/h. The second water tank contains 9 gal of water and is leaking at a constant rate of 7 gal/h. When will the two tanks have the same amount of water? Eplain. Let = the number of hours the tanks are filling and let = the number of gallons in the tank. 87