Unit C Homework Helper Answer Key

Transcription

1 Lesson 5-1 Graphing Proportional Relationships % a. 3. a a. 12 hr 9. a. 4 yr c. B 10. a. 5. a. C c. $ a. 3 wk Yes No digits 11 Grade 8

2 12. 91% a a. 16. a. The graph will be a line that passes through the origin. c. No Number of Week 5.5 sec It will take 11 min and 54.5 sec for the team to complete the 2,000 m course. Lesson 5-2 Linear equations y mx 1. y 46x 2. y 9 10 x 3. Catalina walks faster. 4. a. y 12x 5. a. 21 y 21x 6. y 47x 7. y 1 11 x 8. Elena raises more money per lap. 9. a. Plant 1 grows more per day. Guillermo found the incorrect constant for both plants. 10. a. Store Z charges more per pair of jeans. 11. a. A Parker: 42, Avery: 39 c. Parker reads a greater number of pages per hour. 12. a. y 0.30x Lesson 5-3 The Slope of a Line 1. a. B a. D a. The slope of Line 1 is 2. The slope of Line 2 is 0. Line 1 has the greater slope. 6. A, 0 7. a. undefined Yes a. 4 digits 12 Grade 8

3 10. a a. 2 B 12. a. The slope of Line 1 is 1. The slope of Line 2 is 2. Line 2 has the greater slope. 13. a Line 1 has undefined slope. The slope of the other line is a. The slope of Conveyor 1 is 5. The slope of Conveyor 2 is 4. Conveyor 1 Lesson 5-4 Unit Rates and Slope cm/wk 2. a. 9 cal/min 3. The points (10, 0) and (7, 93) are on the line. The slope of the line is a. Since the relationship is not proportional, use any two points on the line to find the slope a. 64 mph change in x-coordinates She used change in y-coordinates to find a unit rate, not change in y-coordinates change in x-coordinates. 6. a. $750 A unit rate compares a quantity to its unit of measure. Finding the cost of one unit makes it easy to find the cost of multiple units. A unit rate can be used to compare prices or calculate expenses. 7. a a a. Use the points (0, 0) and (4, 5200) to find the slope. Then start at (0, 0), and use the slope to find the next point on the line. 11. a. 3,600 c. 20 hr digits 13 Grade 8

4 12. a. 8,300 parts/hr 5. a. B c. 24 hr 13. a. The slope of the line for Plant 1 is 2. The slope of the line for Plant 2 is 1. The slope of the line for Plant 1 is greater than the slope of the line for Plant 2. Lesson 5-5 The y-intercept of a Line a. B c a. 5 c. B 7. a a. 4. a. 5 A c a. 88 a perfect score on the test c. 2 d. the number of points lost if the student answered a question incorrectly e. Answers will vary. digits 14 Grade 8

5 10. a. 7. a. Plot a point at the y-intercept. 11. a a a. 12 the total cost of the watch with no engraved letters c. 4 Lesson 5-6 Linear Equations: y mx b 1. y 3x 2 2. y 2 5 x 4 3. y 3x a. 4 y 4x 4 6. a. y 1 3 x 2 9. a. y 5x 30 She used the x-intercept instead of the y-intercept 10. a. y 3x 0.50 $ a. y 21x a. y 6x 16 8 Lesson 5-7 Problem Solving 1. Sam runs the fastest. 2. a. y 0.10x a. A Pipe 1 loses more water per hour. total people 4. a. hours They all have the same number of people arriving each hour. 5. a. y 4x 5 7 yr c. B 6. a. y 150x digits 15 Grade 8

6 7. a. C a. Phone 1: y 0.10x 5 Phone 2: y 0.25x 3 Gavin will be able to talk the longest with Phone 1. Lesson 6-1 What is a System of Linear Equations in Two Variables? 1. C, D, F 2. It is only a single equation. 3. Yes 4. B 5. a. C 6. a. A 7. a. n 16 4w n 42 11w The manager switched the constant and coefficient of w in both equations. 8. a. d 58 d 53 3t Lake 2 is deeper. 9. a.replac e x with 6 and y with 13 in each equation. No 10. C 11. C, E 12. B 13. a. C c m c m 14. a. c 42 c 8t 10 Shop N Lesson 6-2 Estimating Solutions of Linear Systems by Inspection 1. One solution 2. One solution 3. No solution 4. Exactly one solution 5. Infinitely many solutions 6. a. No solution 7. A 8. C 9. a. One solution D 10. a. A 11. a. A Exactly one solution 12. The system has infinitely many solutions. 13. a. A A 14. a. A The system has infinitely many solutions. 15. a. infinitely many solutions 16. The system has no solution. Lesson 6-3 Solving Systems of Linear Equations by Graphing 1. a. ( 4, 3) digits 16 Grade 8

7 2. a. c. 15 d. Answers will vary. 7. a. The point where the lines intersect each other (3, 3) 8. a. A 3. a. A c. 4 hr 4. a. Restaurant X c 10 Restaurant Z c 0.6n 2 5. a. c. 12 D c. Bike Shop X c 2.75n 3 Bike Shop Z c 1.75n 7 9. a. A 10. a. ( 3, 3) 6. a. Store W c 5 Store Z c 0.2n 2 c 25 (7, 3) 11. a.online c 15.75n Box Office c 12.75n c n n digits 17 Grade 8

8 12. a. Check students graphs. (0.5, 3.75) Lesson 6-4 Solving Systems of Linear Equations Using Substitution 1. (4, 2) 2. ( 4, 6) 3. Pedro: 1,471 Ricky: 1, River C: 2,800 mi River D: 2,700 mi 5. a. width: 50 ft length: 160 ft 6. a. Q1, 5 8 R 7. a. ( 4, 9) C 8. children: 217 adults: a. (3, 4) 10. a. (2, 1) 11. Speed of plane: mph, Speed of wind: 26.1 mph a. B (5, 2) a. A 40 dimes, 30 nickels 16. a. adult tickets: 100 student tickets: 400 $10 Lesson 6-5 Solving Systems of Linear Equations Using Addition 1. first system: addition second system: substitution 2. A 3. (4, 2) 4. B, C 5. a. B (0, 5) 6. ( 3, 4) 7. a. B The first friend spent $8 and the second friend spent $ , 7 9. Red jar: 13 Blue jar: a. ( 4, 5) 11. Each girl scored 9 points and each boy scored 6 points. 12. B 13. a. ( 4, 1) C 14. Train A: 241 t Train B: 71 t 15. a. C 16. Balloon A: 2 5 gal Balloon B: 1 5 gal 17. x 1 5 y a. x 1 4 y Fish A: 7 Fish B: 3 digits 18 Grade 8

9 Lesson 6-6 Solving Systems of Linear Equations Using Subtraction 1. B 2. A 3. A 4. (4, 3) 5. (3, 5) 6. 2-point shots: 38 1-point shots: large bags of popcorn: 96 small bags of popcorn: a. (2, 1) 9. a. B 10. a. (4, 2) B 11. Fred: 31 years old Natalie: 13 years old 12. 3, length: 7 cm width: 3 cm 14. a. meal: $5 medical kit: $8 $ (4.5, 6) 16. a. D (4, 1) 17. C 18. (4, 2.5) 19. tires purchased from the shop: 161 tires purchased from other shops: 93 Lesson 6-7 Problem Solving 1. C 2. (3, 1) 3. width: 8 ft length: 10 ft 4. a. (2, 1) 5. Q 29 2, 16 5 R 6. a. (9, 8) C 7. width: 320 ft length: 710 ft 8. a. C 9. a. 16, a. A (1, 5) 11. a. C B 12. (6, 1) 13. a. D Roast beef: $5, Turkey: $7 14. a. They will be at the same altitude in 6 min, when their altitude will be 16,200 ft. digits 19 Grade 8