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2.2 – Linear Equations

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

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2.2 – Linear Equations

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  1. 2.2 – Linear Equations

  2. 2.2 – Linear Equations 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 = 7 7a + 4b2 = -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 = 7 7a + 4b2 = -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 = 7 7a + 4b2 = -8 x = 9 y = √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 = 7 7a + 4b2 = -8 x = 9 y = √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 = 7 7a + 4b2 = -8 x = 9 y = √x + 5 6s = -3t – 15 x + 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 = 7 7a + 4b2 = -8 x = 9 y = √x + 5 6s = -3t – 15 x + 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 = 7 7a + 4b2 = -8 x = 9 y = √x + 5 6s = -3t – 15 x + xy = 1 y = ½xy = 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 = 7 7a + 4b2 = -8 x = 9 y = √x + 5 6s = -3t – 15 x + xy = 1 y = ½xy = 1 x

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

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

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

  26. Example 1 State whether each function or equation is linear. If no, explain why. (a) f(x) = 10 – x YES (b) g(x) = x4 – 5

  27. Example 1 State whether each function or equation is linear. If no, explain why. (a) f(x) = 10 – x YES (b) g(x) = x4 – 5 NO

  28. Example 1 State whether each function or equation is linear. If no, explain why. (a) f(x) = 10 – x YES (b) g(x) = x4 – 5 NO; exponent on var.

  29. Example 1 State whether each function or equation is linear. If no, explain why. (a) f(x) = 10 – x YES (b) g(x) = x4 – 5 NO; exponent on var. (c) h(x,y) = 2xy

  30. Example 1 State whether each function or equation is linear. If no, explain why. (a) f(x) = 10 – x YES (b) g(x) = x4 – 5 NO; exponent on var. (c) h(x,y) = 2xy NO

  31. Example 1 State whether each function or equation is linear. If no, explain why. (a) f(x) = 10 – x YES (b) g(x) = x4 – 5 NO; exponent on var. (c) h(x,y) = 2xyNO; multiplying vars.

  32. Standard Form

  33. Standard Form = Ax + By = C

  34. Standard Form = Ax + By = C *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

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