1. 2.2 – Linear Equations

2. Linear equation

3. 2.2 – Linear Equations Linear equation – equation with only addition,

4. 2.2 – Linear Equations Linear equation – equation with only addition, subtraction,

5. 2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication,

6. 2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number.

7. 2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number.

8. 2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number.

9. 2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs.

10. 2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs. 5x – 3y = 7

11. 2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs. 5x – 3y = 7 x = 9

12. 2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs. 5x – 3y = 7 x = 9 6s = -3t – 15

13. 2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs. 5x – 3y = 7 x = 9 6s = -3t – 15 y = ½x

14. 2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs.Non-linear Eqs. 5x – 3y = 7 x = 9 6s = -3t – 15 y = ½x

15. 2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs.Non-linear Eqs. 5x – 3y = 77a + 4b 2 = -8 x = 9 6s = -3t – 15 y = ½x

16. 2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs.Non-linear Eqs. 5x – 3y = 77a + 4b 2 = -8 x = 9 6s = -3t – 15 y = ½x

17. 2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs.Non-linear Eqs. 5x – 3y = 77a + 4b 2 = -8 x = 9y = √x + 5 6s = -3t – 15 y = ½x

18. 2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs.Non-linear Eqs. 5x – 3y = 77a + 4b 2 = -8 x = 9y = √x + 5 6s = -3t – 15 y = ½x

19. 2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs.Non-linear Eqs. 5x – 3y = 77a + 4b 2 = -8 x = 9y = √x + 5 6s = -3t – 15x + xy = 1 y = ½x

20. 2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs.Non-linear Eqs. 5x – 3y = 77a + 4b 2 = -8 x = 9y = √x + 5 6s = -3t – 15x + xy = 1 y = ½x

21. 2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs.Non-linear Eqs. 5x – 3y = 77a + 4b 2 = -8 x = 9y = √x + 5 6s = -3t – 15x + xy = 1 y = ½x y = 1 x

22. 2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs.Non-linear Eqs. 5x – 3y = 77a + 4b 2 = -8 x = 9y = √x + 5 6s = -3t – 15x + xy = 1 y = ½x y = 1 x

23. Example 1State whether each function or equation is linear. If no, explain why.

24. (a) f(x) = 10 – x

25. Example 1State whether each function or equation is linear. If no, explain why. (a) f(x) = 10 – x YES

26. Example 1State whether each function or equation is linear. If no, explain why. (a) f(x) = 10 – x YES (b) g(x) = x 4 – 5

27. Example 1State whether each function or equation is linear. If no, explain why. (a) f(x) = 10 – x YES (b) g(x) = x 4 – 5NO

28. Example 1State whether each function or equation is linear. If no, explain why. (a) f(x) = 10 – x YES (b) g(x) = x 4 – 5NO; exponent on var.

29. Example 1State whether each function or equation is linear. If no, explain why. (a) f(x) = 10 – x YES (b) g(x) = x 4 – 5NO; exponent on var. (c) h(x,y) = 2xy

30. Example 1State whether each function or equation is linear. If no, explain why. (a) f(x) = 10 – x YES (b) g(x) = x 4 – 5NO; exponent on var. (c) h(x,y) = 2xyNO

31. Example 1State whether each function or equation is linear. If no, explain why. (a) f(x) = 10 – x YES (b) g(x) = x 4 – 5NO; exponent on var. (c) h(x,y) = 2xyNO; multiplying vars.

32. Standard Form

33. Standard Form = Ax + By = C

34. *Get x’s and y’s on left side,

35. Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt.

36. Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C.

37. Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3

38. Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3 +2x +2x

39. Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3 +2x +2x 2x + y = 3

40. Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3 +2x +2x 2x + y = 3 A=2

41. Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3 +2x +2x 2x + y = 3 A=2,B=1

42. Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3 +2x +2x 2x + y = 3 A=2,B=1,&C=3

43. Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3(b) ⅜x = 3y + 2 +2x +2x 2x + y = 3 A=2,B=1,&C=3

44. Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3(b) ⅜x = 3y + 2 +2x +2x -3y -3y 2x + y = 3 A=2,B=1,&C=3

45. Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3(b) ⅜x = 3y + 2 +2x +2x -3y -3y 2x + y = 3 ⅜x – 3y = 2 A=2,B=1,&C=3

46. Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3(b) ⅜x = 3y + 2 +2x +2x -3y -3y 2x + y = 3 ⅜x – 3y = 2 A=2,B=1,&C=3 8(⅜x – 3y) = (2)8

47. Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3(b) ⅜x = 3y + 2 +2x +2x -3y -3y 2x + y = 3 ⅜x – 3y = 2 A=2,B=1,&C=3 8(⅜x – 3y) = (2)8 3x – 24y = 16

48. Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3(b) ⅜x = 3y + 2 +2x +2x -3y -3y 2x + y = 3 ⅜x – 3y = 2 A=2,B=1,&C=3 8(⅜x – 3y) = (2)8 3x – 24y = 16 A=3

49. Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3(b) ⅜x = 3y + 2 +2x +2x -3y -3y 2x + y = 3 ⅜x – 3y = 2 A=2,B=1,&C=3 8(⅜x – 3y) = (2)8 3x – 24y = 16 A=3,B=-24

50. Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3(b) ⅜x = 3y + 2 +2x +2x -3y -3y 2x + y = 3 ⅜x – 3y = 2 A=2,B=1,&C=3 8(⅜x – 3y) = (2)8 3x – 24y = 16 A=3,B=-24,&C=16

51. x-intercept

52. x-intercept – (x, 0)

53. x-intercept – (x, 0); y-intercept

54. x-intercept – (x, 0); y-intercept – (0, y)

55. x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation.

56. x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = 0

57. x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = 0 + 12 +12

58. x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = 0 + 12 +12 3x – 4y = 12

59. x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = 0 + 12 +12 3x – 4y = 12 x-int.

60. x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = 0 + 12 +12 3x – 4y = 12 x-int. 3x – 4(0) = 12

61. x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = 0 + 12 +12 3x – 4y = 12 x-int. 3x – 4(0) = 12 (y=0) 3x = 12

62. x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = 0 + 12 +12 3x – 4y = 12 x-int. 3x – 4(0) = 12 (y=0) 3x = 12 3 3

63. x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = 0 + 12 +12 3x – 4y = 12 x-int. 3x – 4(0) = 12 (y=0) 3x = 12 3 x = 4

64. x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = 0 + 12 +12 3x – 4y = 12 x-int. 3x – 4(0) = 12 (y=0) 3x = 12 3 x = 4 (4, 0)

65. x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = 0 + 12 +12 3x – 4y = 12 x-int. 3x – 4(0) = 12 (y=0) 3x = 12 3 x = 4 (4, 0)

66. x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = 0 + 12 +12 3x – 4y = 12 x-int. 3x – 4(0) = 12yint. (y=0) 3x = 12 3 x = 4 (4, 0)

67. x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = 0 + 12 +12 3x – 4y = 12 x-int. 3x – 4(0) = 12yint. 3(0) – 4y = 12 (y=0) 3x = 12 3 x = 4 (4, 0)

68. x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = 0 + 12 +12 3x – 4y = 12 x-int. 3x – 4(0) = 12yint. 3(0) – 4y = 12 (y=0) 3x = 12(x=0) -4y = 12 3 x = 4 (4, 0)

69. x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = 0 + 12 +12 3x – 4y = 12 x-int. 3x – 4(0) = 12yint. 3(0) – 4y = 12 (y=0) 3x = 12(x=0) -4y = 12 3 3 -4 -4 x = 4 (4, 0)

70. x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = 0 + 12 +12 3x – 4y = 12 x-int. 3x – 4(0) = 12yint. 3(0) – 4y = 12 (y=0) 3x = 12(x=0) -4y = 12 3 3 -4 -4 x = 4y = -3 (4, 0)

71. x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = 0 + 12 +12 3x – 4y = 12 x-int. 3x – 4(0) = 12yint. 3(0) – 4y = 12 (y=0) 3x = 12(x=0) -4y = 12 3 3 -4 -4 x = 4y = -3 (4, 0)(0, -3)

72. x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = 0 + 12 +12 3x – 4y = 12 x-int. 3x – 4(0) = 12yint. 3(0) – 4y = 12 (y=0) 3x = 12(x=0) -4y = 12 3 3 -4 -4 x = 4y = -3 (4, 0)(0, -3)

73. (4,0)(0,-3)x-int. =y-int. =

74. (4,0)(0,-3)x-int. =y-int. =

75. (4,0)(0,-3)x-int. =y-int. =