Section 1.3: Graphing Equations

SECTION 1.3 Graphing Equations Section 1.3: Graphing Equations Graphs Intercepts of Graphs Symmetry Circles Graphs Make a table of values and then graph the points from the table. MATH 1310 College Algebra 55

CHAPTER 1 An Introduction to Graphs and Lines Make a table of values and then graph the points from the table. Make a table of values and then graph the points from the table. 56 University of Houston Department of Mathematics

SECTION 1.3 Graphing Equations Additional Example 1: MATH 1310 College Algebra 57

CHAPTER 1 An Introduction to Graphs and Lines Additional Example : 58 University of Houston Department of Mathematics

SECTION 1.3 Graphing Equations Additional Example 3: MATH 1310 College Algebra 59

CHAPTER 1 An Introduction to Graphs and Lines Additional Example 4: 60 University of Houston Department of Mathematics

SECTION 1.3 Graphing Equations Intercepts of Graphs MATH 1310 College Algebra 61

CHAPTER 1 An Introduction to Graphs and Lines Additional Example 1: 6 University of Houston Department of Mathematics

SECTION 1.3 Graphing Equations Additional Example : MATH 1310 College Algebra 63

CHAPTER 1 An Introduction to Graphs and Lines Additional Example 3: 64 University of Houston Department of Mathematics

SECTION 1.3 Graphing Equations Symmetry MATH 1310 College Algebra 65

CHAPTER 1 An Introduction to Graphs and Lines 66 University of Houston Department of Mathematics

SECTION 1.3 Graphing Equations Example Problem: MATH 1310 College Algebra 67

CHAPTER 1 An Introduction to Graphs and Lines Additional Example 1: 68 University of Houston Department of Mathematics

SECTION 1.3 Graphing Equations Additional Example : Additional Example 3: MATH 1310 College Algebra 69

CHAPTER 1 An Introduction to Graphs and Lines 70 University of Houston Department of Mathematics

SECTION 1.3 Graphing Equations Additional Example 4: MATH 1310 College Algebra 71

CHAPTER 1 An Introduction to Graphs and Lines Circles 7 University of Houston Department of Mathematics

SECTION 1.3 Graphing Equations MATH 1310 College Algebra 73

CHAPTER 1 An Introduction to Graphs and Lines Additional Example 1: Additional Example : 74 University of Houston Department of Mathematics

SECTION 1.3 Graphing Equations Additional Example 3: MATH 1310 College Algebra 75

CHAPTER 1 An Introduction to Graphs and Lines 76 University of Houston Department of Mathematics

SECTION 1.3 Graphing Equations Additional Example 4: MATH 1310 College Algebra 77

Exercise Set 1.3: Graphing Equations Determine which of the following points are on the graph of the given equation. 78 3 7 1. x + y = 5; (1, 4), (3, - 7), (, ) 5. x y = 7; (0, -5), (-3, -13), (, - ) 3. xy x + 3 y = 7; (, -5), (-1, 3), ( 6, ) 4. x y = x + y; (3, ), (5, 4), (-7, - 6) 5. x y(3 + xy) = x + 5; (1,1), (-, 3), (-5,0) 6. y ( x xy) = 40; (4, -1), (-3, - ), ( 3, -5) Sketch the graphs of the following equations by plotting points. 7. y = x 5 8. y = 3 x + 4 9. y = x + 3 10. y = x 5 11. y = x 1. y = x + 1 13. 14. 15. 16. y = 3 x 3 y = x 1 y = x 8 y = x Find the x- and y-intercepts of the graph of each of the following equations. 17. y = 4x 5 18. y = 3x 7 19. 5 x + y = 0 0. 3x 4y = 4 1. y = x 16. x = 5 y 3 3. 7 y = x 4. xy = 6 5. y = x + 9 6. y = x + 3 7. x + y = 5 8. 4x y = 9 9. x + xy + 3y = 1 30. 4x 5xy + 3y = 36 In the following questions, only part of the graph is given. Complete each graph using the given symmetry. 31. x-axis 3. y-axis 33. origin 34. x-axis 4 3 1 1 3 4 1 University of Houston Department of Mathematics 4 3 1 3 4 5 4 3 1 4 3 1 1 3 4 1 3 4 5 4 3 1 4 3 1 1 3 4 1 3 4 5 y y y y 4 3 1 4 3 1 1 3 4 1 3 4 5 x x x x

Exercise Set 1.3: Graphing Equations Test the following equations for symmetry with respect to the x-axis, the y-axis, and the origin. Identify the center and radius, and then sketch the graph of the equation. 35. 36. 37. y = x + x x = y + y 3 y = 5x 4 4 55. x + y = 36 56. x + y = 17 57. ( x ) + ( y + 3) = 10 38. 39. 10 y = x 4 5x + x y = y + 40. x y = xy 41. y = 3x + 5x 4. x + y = 5y 43. x + 3 y = 5 44. 3 x 7 y = 4 For each of the following equations: (a) Test the equation for symmetry. (b) Find and plot the intercepts. (c) Plot a few intermediate points in order to complete the graph. (Keep symmetry in mind to minimize the length of this step.) 45. y = x 4 58. ( x + ) + ( y 4) = 4 Write an equation of the circle that satisfies the given conditions. 59. Center (-4, -3); radius 5 60. Center (7, 0); radius 3 61. Center (-, 5); radius 7 6. Center at the origin; radius 3 63. Endpoints of a diameter are (-3, 6) and (5, ) 64. Endpoints of a diameter are (5, -3) and (-9, 11) 65. Center (, 5); passes through (-6, 4) 66. Center (-3, 1); passes through (5, -) 67. Center (-,4); tangent to the x-axis. 68. Center (3, -1); tangent to the y-axis. Write an equation for each of the following circles. 46. 47. 48. y = 5 x y = y = 9 x 5 x 69. 1 y x 3 1 1 3 1 3 49. y = x 4x 50. y = x + 3 The following equations represent circles. Identify the center and radius of each circle. 51. ( x 3) + ( y + 5) = 49 5. ( x + 7) + ( y 1) = 81 53. x + ( y 6) = 8 54. ( x + 8) + y = 3 70. y 8 7 6 5 4 3 1 3 4 3 1 1 3 4 5 6 7 1 x MATH 1310 College Algebra 79

Exercise Set 1.3: Graphing Equations Show that the following equations represent circles by writing them in standard form: ( x h) + ( y k) = r Then identify the center and radius of the circle. 71. x + y + 4x 1y 9 = 0 7. x + y x + 8y 0 = 0 73. x + y 10y + 1 = 0 74. x + y 14x + 39 = 0 75. x + y + x 6y + 7 = 0 1 3 1 3 7 36 76. x + y x + y = 0 80 University of Houston Department of Mathematics