Lesson 2-1 Representing Proportional Relationships 1.. a. 5 hours 8. a. 2. a. 3 cookies 3. a. C c. $26 4. a. 3 years c. B 9. a. 2 weeks 10. a. yes 5. 20% 6. Minutes No; answers will vary. 11. about 90% 12. a. Years 6 years digits Texas 4 Grade 8
13. a. Lesson 2-3 The Slope of a Line 1. a. B D c. no 14. a. 24% 24 ounces Lesson 2-2 Linear Equations: y mx 1. y 46x 2. y 9 10x or y 0.9x 3. 140 pounds per square inch 4. a. y 12x 5. a. m 12 y 12x 6. y 4x. y 1 11 x 8. a. y 9 8x or y 1.125x 18 9. 12 10. 182 pounds 11. 28 12. a. A A; 1 2 or 0.5 c. A; 1 2 x 13. a. y 24x $312 14. $3.0 15. A; 8 16. a. y 3 10x or y 0.3x Check students graphs; explanations will vary. 1 2 2. 2 3. a. D 2 5 4. 2 5. a. The slope of Line 1 is 2. The slope of Line 2 is 0. Line 1 has the greater slope. 6. A, 0. a. undefined Yes 8. 1 2 9. a. 4 10. a. 2 11. 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. 1 2 14. Line 1 has undefined slope. The slope of the other line is 3. 15. a. The slope of Conveyor 1 is 5. The slope of Conveyor 2 is 4. Conveyor 1 digits Texas 5 Grade 8
Lesson 2-4 Unit Rates and Slope 1. 1.5 cm/wk 2. a. 9 cal/min 8. 10.25 9. a. 6.3 10. a. Use the points (0, 0) and (4, 5,200) to find the slope. Then start at (0, 0), and use the slope to find the next point on the line. 3. The points (10, 0) and (, 93) are on the line. The slope of the line is 31. 4. a. Since the relationship is not proportional, use any two points on the line to find the slope. 2 5. 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. $50 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.. a. 11. a. 3,600 c. 20 hr 12. a. 8,300 parts/hr 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. digits Texas 6 Grade 8
Lesson 2-5 The y-intercept of a Line 6. a. 1. 2. 1.5 3. a. B c. 2 4. a. 5 A c. 11 years ago 5. a. B ; 3 3 c. B. a. 4 8. ; 45 9. a. 88 The intercept represents zero questions answered incorrectly. c. 2 d. The slope represents the points lost for each question answered incorrectly. e. Answers will vary. ; 4 digits Texas Grade 8
10. a. 11. a. 14 4 12. a. 12 The intercept represents the cost of the watch with no engraving. c. 4 Lesson 2-6 Linear Equations: y mx b 1. a. 10; 2; 3, 14; 4, 8; 18 T 8 2(p) 2. P 210 (t) 3. y 2x 4 4. y 3 8 x 3 5. a. The y-value is twice the x-value. y 2x 6. a. The y-value is five times the x-value. y 5x. y 0.1x 8 8. y 0.05x 6.95 9. a. y 4x 2 10. a. y 1 4 x 2 11. y 2x 4.6 12. a. The value of x plus 3 equals the value of y. y x 3 13. a. 2 y 3x 2 14. a. 14; 2; 3, 30; 4, 6; 46 The total cost of the rental, C, is 6 plus the product of 8 and the number of hours the paddle boat is rented, r. c. C 6 8(r) 15. a. y 5x 6 y 2x 4 Lesson 2- Distinguishing Between Proportional and Non-Proportional Situations 1. 69 3 23 1 ; 92 4 23 1 2. a. y 2x 53 No c. 43 F d. C 3. 5 1 ; 5 1 ; 5 1 4. Yes 5. a. C 14 c. 5 1 2 d. 5 1 2 digits Texas 8 Grade 8
6. a. x 5 No. a. 10; 10; 10; 10 B 8. a. y x 4 5 No 9. a. 5; 21; 1 ; 1 10. 1 16 ; 23 4 1 4 ; 1 4 Lesson 2-8 Additional Problem Solving 1. They all run the same speed. 2. a. They all charge the same amount. Check students graphs; explanations will vary. 3. a. Yes cos t ; explanations will vary. dozen 4. a. y 3x 0.5 $9.50 5. a. B Pipe 1 6. a. 110 They all have the same number of people arriving per hour.. a. Find the ratio of hours to yards for each row in the table. no 8. proportional Lesson 3-1 Recognizing a Function 1. D 2. 3. a. No 4. No 5. a. 3 1 5 19 11 23 13 29 Yes 1 2 4 5 9 13 16 6 1 5 9 10 10 32 6. No. No 8. a. {(49, 13), (61, 36), (10, 2), (6, 52), (23, 52)} 9. Yes; answers will vary. 10. a. Yes c. A 11. a. Relation 2, Relation 3 12. Yes digits Texas 9 Grade 8
13. a. 14. a. The relation is not a function. Yes 15. a. A 16. a. 3 2 12 14 3 6 9 15 24 42 39 8 11 5 10 10 20 15 30 20 40 25 Yes 1. a. 3 6 Lesson 3-2 Representing a Function 1. a. 2; (1, 2); 3; (2, 3); 4; (3, 4) y x 1 c. 2. a. 0; (0, 0); 14; (16, 14); 21; (24, 21) y 8 x c. 3. a. 240 km in 2 hours 220; (2, 220); 330; (3, 330); 440; (4, 440) c. y 120x d. 15 16 6 14 14 3 15 16 c. Only Relation P is a function. digits Texas 10 Grade 8
4. a. 20 feet in 3 hours 20; (3, 20); 360; (4, 360); 900; (10, 900) c. y 90x d. Lesson 3-3 Linear Functions 1. a. e. 18 hours 5. 5; 3; 1; 3 6. a. 0; 3; 5; 12. a. equation y x 3 6 c. 6; (0, 6); ; (3, ); 8; (6, 8) d. 8. a. B 9; ; 4; 3; 0 no 2. 3 3. B 4. B 5. a. 3 Every minute the student has 3 fewer problems to do. 6. a. B. a. 1 3.5 8. a. 2 9. a. A, C, and E 0.3 c. 0.3 10. a. Answers will vary. c. no digits Texas 11 Grade 8
11. a. 2.2 Number of ounces of water added to can every second c. 39 seconds Lesson 3-4 Nonlinear Functions 1. Yes 2. a. II and III I 3. a. I and III B 4. No 5. a. A 6. a. Function II. a. C Lesson 3-5 Additional Problem Solving 1. a. 5, 2, 1, 4, 4. a. Nonlinear Check students work. 5. a. Nonlinear 352 6. a. D Nonlinear. a. B 2, 4.5, 1, 5.25, 0, 6, 1, 6.5, 2, 6.5 c. Check students work. d. B 8. a. Tables will vary. c. Nonlinear; explanations will vary. c. Linear; explanations will vary. 2. Nonlinear 3. a. 20, 5, 0, 5, 20 c. D d. Answers will vary. digits Texas 12 Grade 8