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6. x + y = –1 Chapter Review 1. Determine whether the relation {(5, 3), (–5, 4), (4, 2), (4, 1)} is a function. Explain. ANSWER: No; The domain value 4 is paired with 2 range values, 1 and 2. ANSWER: Sample answer: (–1, 0), (0,–1), (1, –2), (2, –3) Graph each equation. 7. y = –2x ANSWER: 2. Use the table that shows the cost of gas in different years. Is the relation a function? Explain. ANSWER: Yes; each domain value is paired with only one range value. Find four solutions of each equation. Write the solution as ordered pairs. 3. y = –5x ANSWER: Sample answer: (–1, 5), (0, 0), (1, –5), (2, –10) 8. y = x + 5 ANSWER: 4. y = 4x ANSWER: Sample answer: (–1, –4), (0, 0), (1, 4), (2, 8) 5. y = x + 9 ANSWER: Sample answer: (–1, 8), (0, 9), (1, 10), (2, 11) 6. x + y = –1 ANSWER: Sample answer: (–1, 0), (0,–1), (1, –2), (2, –3) Graph each equation. 7. y = –2x ANSWER: 9. Each small smoothie x costs $1.50, and each large smoothie y costs $3. Find two solutions of 1.5x + 3y = 12 to determine how many of each type Lisa can buy with $12. ANSWER: Sample answer: (0, 4) means she can buy 0 small smoothies and 4 large smoothies with $12; (6, 1) means she can buy 6 small smoothies and 1 large smoothie with $12. 10. Find the constant rate of change between the quantities in the table below. ANSWER: $7.75 per hour eSolutions Manual - Powered by Cognero 8. y = x + 5 Page 1 Find the slope of the line that passes through each pair of points. 11. F(0, 1), G(6, 4) ANSWER: No; the ratio is different for each pair of values, and the line does not pass through (0, 0). ANSWER: Chapter Review $7.75 per hour Find the slope of the line that passes through each pair of points. 11. F(0, 1), G(6, 4) ANSWER: State the slope and the y-intercept of the graph of each equation. 17. y = 4x + 7 ANSWER: 4; 7 18. y = 12. A(–3, 7), G(5, –1) ANSWER: –1 x ANSWER: – 13. A lizard is crawling up a hill that rises 5 feet for every horizontal change of 30 feet. Find the slope. ANSWER: ;0 19. 5x + y = 0 ANSWER: –5; 0 20. –x + y = –8 The cost of renting a paddle boat varies directly with the number of hours, as shown in the table. ANSWER: 1; –8 21. y = –8x – 7 14. Write an equation that relates the number of hours with the cost. ANSWER: y = 9x ANSWER: –8; –7 22. 4x – y = 6 15. Find the cost of renting a paddle boat for 7 hours. ANSWER: $63 16. The temperature for one day is shown in the graph. Determine whether the relationship between the temperature and the time is a direct variation. ANSWER: 4; –6 Graph each equation using the slope and yintercept. 23. y = –x + 4 ANSWER: ANSWER: No; the ratio is different for each pair of values, and the line does not pass through (0, 0). 24. y = 2x – 6 State the slope and the y-intercept eSolutions Manual - Powered by Cognero of each equation. 17. y = 4x + 7 of the graph ANSWER: Page 2 Chapter Review 24. y = 2x – 6 ANSWER: 27. A balloon is rising above the ground. The height in feet y of the balloon can be given by y = 7 + 2x, where x represents the time in seconds. State the slope and y-intercept of the graph of the equation. Describe what they represent. ANSWER: Slope: 2; y-intercept: 7; the slope 2 represents the ascent in ft per second. The y-intercept 7 represents the initial altitude in ft before the balloon is released. 28. Jacob is ordering DVDs from a Web site. The site charges a flat rate for shipping, no matter how many DVDs he buys. The total cost y of Jacob’s order is given by y = 9x + 5, where x represents the number of DVDs he buys. State the slope and y-intercept of the equation. Describe what they represent. 25. y = x–3 ANSWER: ANSWER: Slope: 9; y-intercept: 5; the slope represents the cost of each DVD ($9); the y-intercept represents the shipping fee ($5). Solve each system of equations by graphing. 29. y = x y= x–1 ANSWER: 26. y = x+5 ANSWER: 30. y = x + 2 y = 3x ANSWER: 27. A balloon is rising above the ground. The height in feet y of the balloon can be given by y = 7 + 2x, where x represents the time in seconds. State the eSolutions Manual - Powered by Cognero slope and y-intercept of the graph of the equation. Describe what they represent. Page 3 Chapter Review 30. y = x + 2 y = 3x ANSWER: ANSWER: Sample answer: y = 2x, x + y = 24; x = 8, y = 16; the café sold 8 vanilla smoothies and 16 strawberry smoothies. Solve each system algebraically. 35. y = 4 y = 3x – 11 ANSWER: (5, 4) 36. y = 6 – x x = –1 ANSWER: (–1, 7) 37. –5x + y = 2 –3x + 6y = 12 ANSWER: (0, 2) 31. y = 2x + 1 x + y = –2 ANSWER: (–1, –1) 32. 5x – 3y = –3 y = –x + 1 ANSWER: (0, 1) 33. The sum of two numbers is 9, and the difference of the numbers is 1. Write a system of equations to represent this situation. Then solve the system to find the numbers. ANSWER: Sample answer: x + y = 9, x – y = 1; 5 and 4; x = 5; y=4 34. A café sells strawberry smoothies and vanilla smoothies. On Monday, the café sold twice as many strawberry smoothies as vanilla smoothies. The total number of smoothies sold was 24. Write a system of equations to represent this situation. Then solve the system and explain what the solution means. ANSWER: Sample answer: y = 2x, x + y = 24; x = 8, y = 16; the café sold 8 vanilla smoothies and 16 strawberry smoothies. Solve each- Powered systembyalgebraically. eSolutions Manual Cognero 35. y = 4 y = 3x – 11 38. –4x + y = 6 –5x – y = 21 ANSWER: (–3, –6) 39. 2x – 4y = 6 3x – 5y = 11 ANSWER: (7, 2) 40. 8y = 6 – 2x x = 3 – 4y ANSWER: infinitely many solutions 41. 7x – 3y = –4 7x = –2 + 3y ANSWER: no solution 42. 2x + y = 3 y = –3x + 7 ANSWER: (4, –5) 43. One number subtracted from three times another number is 11. The sum of the numbers is 1. Write and solve a system of equations to represent this situation. Interpret the solution. ANSWER: 3x – y = 11; x + y = 1; (3, –2); One number is 3; the Page 4 other number is –2. 44. Tickets to a museum cost $3 for children and $8 for 42. 2x + y = 3 y = –3x + 7 ANSWER: Chapter Review (4, –5) 43. One number subtracted from three times another number is 11. The sum of the numbers is 1. Write and solve a system of equations to represent this situation. Interpret the solution. ANSWER: 3x – y = 11; x + y = 1; (3, –2); One number is 3; the other number is –2. 44. Tickets to a museum cost $3 for children and $8 for adults. A group of four visitors to the museum spent a total of $22 on tickets. Write and solve a system of equations to represent this situation. Interpret the solution. ANSWER: x + y = 4; 3x + 8y = 22; (2, 2); There were two children and two adults in the group. eSolutions Manual - Powered by Cognero Page 5