Section 3.2 Graphing Linear Equations 223 SECTION 3.2 EXERCISE SET Write About It! Use complete sentences to explain the meaning of each term or process. 1. Graph a line by point-plotting. 2. Graph a line by using the x-intercept and y-intercept. 3. Which method is easier to use with the equation y = -4x + 2? Which method is easier to use with the equation 4x - 3y = -12? Determine if each statement is true or false. If a statement is false, provide an explanation. 4. The equation y = 3x - 4 is equivalent to 3x - y = -4. 5. The graph of the equation 7x - y = 14 passes through the point (0, 2). 6. The x-intercept of y = 8x - 24 is (0, -24). 7. The graph of the equation x = -2 has a y-intercept at (0, -2). 8. The graph of the equation y = 3 has no x-intercept. 9. The graph of the equation y = 5x passes through the origin. 10. The graph of the equation 2x + 3y = 0 passes through the origin. Practice Makes Perfect! Determine if the equation is a linear equation in two variables. (See Objective 1.) 11. 4x + 5y = 6 12. 3x -2y = -12 13. x2 + y = 4 14. x + y2 = 9 15. x = 2y 16. y=- 4 3 x 17. x 2 - y 4 = 1 8 18. x2 + y2 = 4 19. x = 3 20. y = -1 Make a table of at least three ordered pairs that are solutions of the equation and use these points to graph each equation. (See Objective 2.) 21. x + 4y = 8 22. x - 6y = 12 23. 3x + y = -6 24. 5x + y = 10 25. y = -x + 1 26. y = -x - 3 27. y = 2x - 4 28. y = -2x + 3 29. y = 2 3 x - 6 30. y=- 2 5 x + 4 31. y=- 1 4 x + 2 32. y = 5 6 x - 1 Use the intercepts to graph each equation. Label the intercepts as ordered pairs on the graph. (See Objective 3.) 33. x - 2y = 6 34. x + 6y = 6 35. 7x - y = -7 36. 2x + y = -4 37. y + 2x = 0 38. y - 2x = 0 39. y = -x + 4 40. y = -x - 7 41. y = 4x - 5 42. y = -6x + 3 43. y = 1 2 x + 5 44. y=- 3 4 x + 6 Graph each equation. (See Objective 4.) 45. y = 6 46. y = -5 47. x = -7 48. x = 4 49. 8y - 2 = 0 50. 6y + 3 = 0 51. 2x + 4 = 0 52. 3x - 9 = 0 53. 4y + 3 = 0 54. 2y - 7 = 0 55. 1 2 x + 5 = 0 56. - 3 4 x + 8 = 0 57. 1 3 y - 2 = 0 58. - 3 4 y + 1 = 0 Use the equation to answer each question. (See Objective 5.) 59. The median annual income for men with a master’s degree is given by the equation y = 1873x + 49,217, where x is the number of years after 1991. (Source: www .infoplease.com) a. Find the y-intercept and interpret its meaning. b. Find the median annual income for men in 2001. c. Find the expected median annual income for men in 2012. 60. The median annual income for women with a master’s degree is given by the equation y = 1335x + 35,660, where x is the number of years after 1991. (Source: www .infoplease.com) a. Find the y-intercept and interpret its meaning. b. Find the median annual income for women in 2001. c. Find the expected median annual income for women in 2012. 61. The average retail price, in cents per kilowatt-hour, of electricity for residential use can be modeled by the equation y = 0.395x + 8.154, where x is the number of years after 2001. (Source: www.eia.gov) a. Find the y-intercept and interpret its meaning. b. Find the average retail price of electricity for residential use in 2010. c. Find the expected average retail price of electricity for residential use in 2015. 62. The average domestic first purchase price of crude oil, in dollars per barrel, can be modeled by the equation y = 6.679x + 16.173, where x is the number of years after 2000. (Source: www.eia.gov) a. Find the y-intercept and interpret its meaning. b. Find the average domestic first purchase price of crude oil in 2010. c. Find the expected average domestic first purchase price of crude oil in 2013.
hendricks_beginning_intermediate_algebra_1e_ch1_3
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