Standard form of a linear equation is Ax + By = C Lesson 6.3 Standard form of a linear equation is Ax + By = C Where A, B, and C are real numbers and A and B are not both zero. X-intercept—is the x-coordinate of the point where a line crosses the x-axis.

Find the x- and y-intercepts of 2x + 5y = 6. Standard Form ALGEBRA 1 LESSON 6-3 Find the x- and y-intercepts of 2x + 5y = 6. Step 1  To find the x-intercept, substitute 0 for y and solve for x. 2x + 5y = 6 2x + 5(0) = 6 2x = 6 x = 3 The x-intercept is 3. Step 2  To find the y-intercept, substitute 0 for x and solve for y. 2x + 5y = 6 2(0) + 5y = 6 5y = 6 y = The y-intercept is . 6 5 6-3

You Try: Find the x and y intercept of 4x – 9y = -12 Find x 4x – 9 (0) = -12 4x = -12 4 4 x = -3 Find y 4(0) -9 y = -12 -9y = -12 -9 -9 Y = 4/3 or 1 1/3

Graph 3x + 5y = 15 using intercepts. Standard Form ALGEBRA 1 LESSON 6-3 Graph 3x + 5y = 15 using intercepts. Step 1  Find the intercepts. 3x + 5y = 15 3x + 5(0) = 15 Substitute 0 for y. 3x = 15 Solve for x. x = 5 3(0) + 5y = 15 Substitute 0 for x. 5y = 15 Solve for y. y = 3 Step 2  Plot (5, 0) and (0, 3). Draw a line through the points. 6-3

0 • x + 1 • y = 4 Write in standard form. For all values of x, y = 4. ALGEBRA 1 LESSON 6-3 a. Graph y = 4 b. Graph x = –3. 0 • x + 1 • y = 4 Write in standard form. For all values of x, y = 4. 1 • x + 0 • y = –3 Write in standard form. For all values of y, x = –3. 6-3

You try: Graph: Y = 5 Write in standard form: 0· x + 1· y = 5 For all values of x, y = 5 X = -4 1 · x + 0 · y = -4 For every y x = -4

Write y = x + 6 in standard form using integers. ALGEBRA 1 LESSON 6-3 Write y = x + 6 in standard form using integers. 2 3 y = x + 6 2 3 3y = 3( x + 6 ) Multiply each side by 3. 3y = 2x + 18 Use the Distributive Property. –2x + 3y = 18 Subtract 2x from each side. The equation in standard form is –2x + 3y = 18. 6-3

You try: Write y = -2/5 x + 1 in standard form using integers. (-5) y = -5(-2/5x + 1) -5y = -2x + -5 +2x +2x 2x + -5y =-5

Define: Let = the hours mowing lawns. Standard Form ALGEBRA 1 LESSON 6-3 Write an equation in standard form to find the number of hours you would need to work at each job to make a total of $130. Define:  Let = the hours mowing lawns. Let = the hours delivering newspapers. x y Amount Paid per hour Job Mowing lawns $12 Delivering newspapers Relate: $12 per h   plus $5 per h equals   $130 mowing delivering $5 Write:  12 + 5 = 130 x y The equation standard form is 12x + 5y = 130. 6-3

Standard Form pages 301–303 Exercises 1. 18; 9 2. 3; –9 3. –6; 30 ALGEBRA 1 LESSON 6-3 pages 301–303  Exercises 1. 18; 9 2. 3; –9 3. –6; 30 4. ; –3 5. – ; – 6. –8; 12 7. 6; 4 8. ; –2 9. –5; 4 10. B 11. C 12. A 13. 14. 15. 16. 17. 18. 19. horizontal 20. vertical 21. horizontal 22. vertical 23. 24. 3 2 9 2 3 2 4 7 6-3

Standard Form 25. 26. 27. –3x + y = 1 28. 4x – y = 7 29. x – 2y = 6 ALGEBRA 1 LESSON 6-3 25. 26. 27. –3x + y = 1 28. 4x – y = 7 29. x – 2y = 6 30. –2x + 3y = 15 31. –3x – 4y = 16 32. –4x – 5y = 35 33. –14x + 4y = 1 34. 4x + 10y = 1 35. 3x + y = 0 36. a. Answers may vary. Sample: x = no. of cars; y = no. of vans or trucks b. 5x + 6.5y = 800 37. a. Answers may vary. Sample: x = time walking; y = time running b. 3x + 8y = 15 38. 39. 40. 41. 42. 6-3

Standard Form 47. a. 3x + 7y = 28 43. 51. y = – x – 3 b. 7 oz 44. ALGEBRA 1 LESSON 6-3 47. a. 3x + 7y = 28 b. 7 oz 48. 4.29x + 3.99y = 30 49. 50. 4 5 43. 44. 45. 51. y = – x – 3 52. y = x – 5 9 3 y = x + 10 4 5 46. y = x + 3 6 7 6-3

Sample: slope-intercept form when comparing the Standard Form ALGEBRA 1 LESSON 6-3 53. y = – x – 8 54. y = x – 16 11 1 9 2 3 55. Answers may vary. Sample: slope-intercept form when comparing the steepness of two lines; standard form when making quick graphs 56. Answers may vary. Sample: 0x + 0y = 0, no linear equation exists. 57. –3x instead of 3x 58. y = 2 59. y = –2 60. x = 1 61. x = –2 62. a. 200s + 150a = 1200 b. Answers may vary. Sample: s = $2.00, a = $5.33; s = $3.00, a = $4.00; s = $6.00, a = $0.00 s = $3.00 and a = $4.00 because they are whole dollar amounts, and adults pay more. 63. y = x + 4 5 6-3

three of the following: 1 Supreme, 35 Prestige; [3] correct equation Standard Form ALGEBRA 1 LESSON 6-3 64.   square 65. a. b. – ; – c. Answers may vary. Sample: The x- and y-intercepts of 2x + 3y = 18 are 3 times those of 2x + 3y = 6. 66. C 67. H 68. [2] y = x + 1; x – 4y = –4 [1] correct slope- intercept equation 69. [4] a. 48x + 56y = 2008 b. c. Answers will include three of the following: 1 Supreme, 35 Prestige; 8 Supreme, 29 Prestige; 15 Supreme, 23 Prestige; 22 Supreme, 17 Prestige; 29 Supreme, 11 Prestige; 36 Supreme, 5 Prestige [3] correct equation and graph [2] wrong equation, but a corresponding correct graph [1] Correct equation only 70. yes 71. no 72. no 73. 74. 75. 4 76. 2.25 77. –0.5 78. –21 1 4 1 36 1 12 2 3 2 3 6-3