Section 3.4 More About Slope 247 Determine if the two lines are parallel, perpendicular, or neither. (See Objective 3.) 15. y = 4 3 x - 5 and y = 4 3 x + 5 16. y = -6x + 1 and y = -6x 17. y = 9x + 3 and y = -9x - 7 18. y = 7x + 2 and 7x - y = 14 19. x + 3y = -6 and y = 3x + 4 20. 2x - y = 8 and 4x - 2y = -4 21. x + 5y = 10 and 3x - 15y = 0 22. y = 3 and y = 3x 23. x = 2 and 5x + 2 = 0 24. y - 5 = 0 and y = -2 25. y = 2x - 4 and y = -2x + 3 26. y = -2x - 4 and y = 1 2 x + 5 27. y = 5x - 4 and y=- 1 5 x 28. 3x + y = 6 and y = 3x - 4 29. 3x + y = 6 and y=- 1 3 x - 6 30. 4x + 3y = 6 and y = 3 4 x - 5 31. x + 7y = 21 and 7x - y = -14 32. 2x + 5y = -10 and 5x + 2y = 20 33. x = 5 and y = 2 34. y = -4 and y = 1 4 x Graph the given line and the line that is parallel to it through the given point. (See Objective 4.) 35. y = 2x - 4; (-2, 2) 36. y = -3x + 3; (0, -2) 37. y = 1 5 x - 1; (5, 5) 38. y=- 2 3 x + 4; (0, 0) 39. x + y = 4; (0, -2) 40. x - y = 3; (-3, -1) 41. x = 2; (-1, 4) 42. x = -3; (4, 2) 43. y = -4; (0, 3) 44. y = 1; (-4, -2) Graph the given line and the line that is perpendicular to it through the given point. (See Objective 4.) 45. y = 2x - 4; (-2, 2) 46. y = -3x + 3; (0, -2) 47. y = 1 5 x - 1; (5, 5) 48. y=- 2 3 x + 4; (0, 0) 49. x + y = 4; (0, -2) 50. x - y = 3; (-3, -1) 51. x = 2; (-1, 4) 52. x = -3; (4, 2) 53. y = -4; (0, 3) 54. y = 1; (-4, -2) Mix ’Em Up! Solve each problem. 55. What is the pitch of a roof that rises vertically 12 in. for each 5 in. it extends horizontally? 5. The owner of a limousine rental company purchases a stretch limousine for $110,000. For tax purposes, the owner uses straight-line depreciation for reporting the value of the limousine. The depreciated value of the limousine is given by y = -22,000x + 110,000, where x is the age of the limousine in years. 6. The number of U.S. households with cable television is approximated by y = 2.3x + 17.3 (in millions), where x is the number of years after 1977. (Source: The World Almanac and Book of Facts 2006) 7. The percentage of eighth-graders who reported using alcohol is given by y = -0.7x + 27, where x is the number of years after 1993. (Source: The World Almanac and Book of Facts 2006) 8. The average cost, in dollars, of higher education at 2-yr institutions can be approximated by the equation y = 334x + 5252, where x is the number of years after 1999. (Source: www.infoplease.com) Practice Makes Perfect! Determine the slope described in each situation. (See Objective 2.) 9. Traversing the Cooper River in Charleston, South Carolina, the 13,200-ft Cooper River Bridge is North America’s longest cable-stayed bridge. The average grade of the bridge is 4.1%. The steepest part of the bridge occurs on a section that is three-tenths of a mile long (1584 ft) with a vertical rise of 88.7 ft. What is the grade of the bridge on this section? (Source: www .cooperriverbridge.org, http://www.cooperriverbridge.org) 10. Filbert Street in San Francisco, California, is one of the steepest streets in the city and in America. The street rises 63 ft for a 200-ft run. What is the grade of the street? Express the grade as a fraction and a percentage. (Source: http://wikitravel.org/en/San_Francisco) 11. A roof rises vertically 12 in. for each 12 in. it extends horizontally. What is the pitch of the roof? 12. What is the pitch of a roof that rises 6 in. for each 12 in. it extends horizontally? 13. The American National Standards Institute facilitates the development of national standards for the steepness of wheelchair ramps. The national standard for constructing wheelchair ramps specifies that a slope of 1 1 is preferable, but a slope of is acceptable when 12 8 the former is not possible. If a builder constructs a wheelchair ramp with a rise of 3 in. for every run of 24 in., does the slope of the ramp meet the guidelines? 14. If a door is 15 in. above the ground, how long must the wheelchair ramp be for its slope to be 1 12 ? Express answer in inches and feet.
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