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By Sapagovas M.P.

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29. 13, 42 30. 15, 32 34. 1-1, -12 31. 1-2, 12 35. 1-3, -42 32. 14, -22 36. 14, 02 33. 15, -22 37. 10, -32 38. 1-3, 02 In Problems 39–50, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, or the origin. 39. 40. y 3 Ϫ3 3x –3 44. y 3 3x –3 y 4 1 ␲ Ϫ␲ Ϫ –– 3x 2 ␲ –– 2 Ϫ1 ␲x Ϫ3 3 x Ϫ4 45. y 3 48. 40 3x Ϫ6 6 Ϫ6 Ϫ40 49. y 3 50. 8 Ϫ2 Ϫ3 x 3x –3 y 3 y 46. y 6 Ϫ3 3x –3 –3 47. 42. y Ϫ3 –3 43. 41. y 3 2 4 Ϫ4 4 3x Ϫ3 Ϫ8 Ϫ3 Ϫ4 Ϫ3 In Problems 51–54, draw a complete graph so that it has the type of symmetry indicated.

The graph of an equation in two variables x and y consists of the set of points in the xy-plane whose coordinates 1x, y2 satisfy the equation. EXAMPLE 1 Determining Whether a Point Is on the Graph of an Equation Determine if the following points are on the graph of the equation 2x - y = 6. (a) 12, 32 Solution (b) 12, -22 (a) For the point 12, 32, check to see if x = 2, y = 3 satisfies the equation 2x - y = 6. 2x - y = 2122 - 3 = 4 - 3 = 1 Z 6 The equation is not satisfied, so the point 12, 32 is not on the graph of 2x - y = 6.

1x + 32 = 12 2 Simplify. x + 3 = ; 212 Apply the Square Root Method. x = -3 ; 2 23 Solve for x. 46. To find the y-intercepts, if any, let x = 0. 65. Look back at Figure 25 to verify the approximate locations of the intercepts. ᭹ Now Work PROBLEM 95(c) 8 Work with the General Form of the Equation of a Circle If we eliminate the parentheses from the standard form of the equation of the circle given in Example 14, we get 1x + 322 + 1y - 222 = 16 x2 + 6x + 9 + y2 - 4y + 4 = 16 which, upon simplifying, is equivalent to x2 + y2 + 6x - 4y - 3 = 0 (2) It can be shown that any equation of the form x2 + y2 + ax + by + c = 0 has a graph that is a circle, or a point, or has no graph at all.

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