Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

AA Section 3-5

692 views

Published on

Finding an Equation of a Line

  • Be the first to comment

  • Be the first to like this

AA Section 3-5

  1. 1. Section 3-5 Finding the Equation of a Line ...or th e Po in t-S lo pe Th eo re m se ct io n
  2. 2. Warm-up Write an equation for the line through the pair of points a. (5, 9), (5, -2) b. (9, 1), (6, 4)
  3. 3. Warm-up Write an equation for the line through the pair of points a. (5, 9), (5, -2) b. (9, 1), (6, 4) x=5
  4. 4. Warm-up Write an equation for the line through the pair of points a. (5, 9), (5, -2) b. (9, 1), (6, 4) x=5 y = -x + 10
  5. 5. Warm-up Write an equation for the line through the pair of points a. (5, 9), (5, -2) b. (9, 1), (6, 4) x=5 y = -x + 10 Not quite sure how this is done? We’ll see two ways today
  6. 6. Question What determines a line?
  7. 7. Question What determines a line? Two points
  8. 8. Question What determines a line? Two points ...and once we have two points, we can find an equation
  9. 9. Example 1 The formula relating blood pressure and age is linear. Normal systolic blood pressures are 110 for a 20 year old and 130 for a 60 year old. Graph the line and find an equation where blood pressure B is a function of age A.
  10. 10. Example 1 The formula relating blood pressure and age is linear. Normal systolic blood pressures are 110 for a 20 year old and 130 for a 60 year old. Graph the line and find an equation where blood pressure B is a function of age A. 130.0 Blood Pressure 97.5 65.0 32.5 0 0 15 30 45 60 Age
  11. 11. Example 1 (con’t) (20, 110), (60, 130)
  12. 12. Example 1 (con’t) (20, 110), (60, 130) 130 − 110 m= 60 − 20
  13. 13. Example 1 (con’t) (20, 110), (60, 130) 130 − 110 20 m= = 60 − 20 40
  14. 14. Example 1 (con’t) (20, 110), (60, 130) 130 − 110 20 1 m= = = 60 − 20 40 2
  15. 15. Example 1 (con’t) (20, 110), (60, 130) 130 − 110 20 1 m= = = 60 − 20 40 2 B= 2 A+b 1
  16. 16. Example 1 (con’t) (20, 110), (60, 130) 130 − 110 20 1 m= = = 60 − 20 40 2 B= 2 A+b 1 110 = (20) + b 1 2
  17. 17. Example 1 (con’t) (20, 110), (60, 130) 130 − 110 20 1 m= = = 60 − 20 40 2 B= 2 A+b 1 110 = (20) + b 1 2 110 = 10 + b
  18. 18. Example 1 (con’t) (20, 110), (60, 130) 130 − 110 20 1 m= = = 60 − 20 40 2 B= 2 A+b 1 110 = (20) + b 1 2 110 = 10 + b b = 100
  19. 19. Example 1 (con’t) (20, 110), (60, 130) 130 − 110 20 1 m= = = 60 − 20 40 2 B= 2 A+b 1 110 = (20) + b 1 2 110 = 10 + b b = 100 B = 2 A + 100 1
  20. 20. Example 1 (con’t) (20, 110), (60, 130) 130 − 110 20 1 m= = = 60 − 20 40 2 B= 2 A+b 1 110 = (20) + b 1 2 110 = 10 + b b = 100 B = 2 A + 100 1 There has to be a better way!
  21. 21. Point-Slope Theorem
  22. 22. Point-Slope Theorem If a line contains (x1, y1) and has slope m, then it has the equation y - y1 = m(x - x1)
  23. 23. Point-Slope Theorem If a line contains (x1, y1) and has slope m, then it has the equation y - y1 = m(x - x1) (In other words, you need a point and the slope)
  24. 24. Example 2 Find an equation for the line through (-3, 6) and (5, 0) using the point-slope theorem.
  25. 25. Example 2 Find an equation for the line through (-3, 6) and (5, 0) using the point-slope theorem. 6−0 m= −3 − 5
  26. 26. Example 2 Find an equation for the line through (-3, 6) and (5, 0) using the point-slope theorem. 6−0 6 m= = −3 − 5 −8
  27. 27. Example 2 Find an equation for the line through (-3, 6) and (5, 0) using the point-slope theorem. 6−0 6 3 m= = =− −3 − 5 −8 4
  28. 28. Example 2 Find an equation for the line through (-3, 6) and (5, 0) using the point-slope theorem. 6−0 6 3 m= = =− −3 − 5 −8 4 y − y1 = m(x − x1 )
  29. 29. Example 2 Find an equation for the line through (-3, 6) and (5, 0) using the point-slope theorem. 6−0 6 3 m= = =− −3 − 5 −8 4 y − y1 = m(x − x1 ) 3 y − 0 = − 4 (x − 5)
  30. 30. Example 2 Find an equation for the line through (-3, 6) and (5, 0) using the point-slope theorem. 6−0 6 3 m= = =− −3 − 5 −8 4 y − y1 = m(x − x1 ) 3 y − 0 = − 4 (x − 5) 3 15 y=−4x+ 4
  31. 31. When dealing with real world situations, deal with the problem as we always have: find the equation first, then answer the question.
  32. 32. Example 3 The lightest recommended weight for a Martian with height 4’10” is 109 lbs. This weight increases 2 lbs/in to a height of 5’1” and then goes up 3 lbs/in to a height of 6’ which is tall for a Martian. a. Graph the situation
  33. 33. Example 3 The lightest recommended weight for a Martian with height 4’10” is 109 lbs. This weight increases 2 lbs/in to a height of 5’1” and then goes up 3 lbs/in to a height of 6’ which is tall for a Martian. a. Graph the situation First, we need to convert all heights to inches
  34. 34. Example 3 The lightest recommended weight for a Martian with height 4’10” is 109 lbs. This weight increases 2 lbs/in to a height of 5’1” and then goes up 3 lbs/in to a height of 6’ which is tall for a Martian. a. Graph the situation First, we need to convert all heights to inches 4’10” =
  35. 35. Example 3 The lightest recommended weight for a Martian with height 4’10” is 109 lbs. This weight increases 2 lbs/in to a height of 5’1” and then goes up 3 lbs/in to a height of 6’ which is tall for a Martian. a. Graph the situation First, we need to convert all heights to inches 4’10” = 4(12) +10 =
  36. 36. Example 3 The lightest recommended weight for a Martian with height 4’10” is 109 lbs. This weight increases 2 lbs/in to a height of 5’1” and then goes up 3 lbs/in to a height of 6’ which is tall for a Martian. a. Graph the situation First, we need to convert all heights to inches 4’10” = 4(12) +10 = 58”
  37. 37. Example 3 The lightest recommended weight for a Martian with height 4’10” is 109 lbs. This weight increases 2 lbs/in to a height of 5’1” and then goes up 3 lbs/in to a height of 6’ which is tall for a Martian. a. Graph the situation First, we need to convert all heights to inches 4’10” = 4(12) +10 = 58” 5’1” =
  38. 38. Example 3 The lightest recommended weight for a Martian with height 4’10” is 109 lbs. This weight increases 2 lbs/in to a height of 5’1” and then goes up 3 lbs/in to a height of 6’ which is tall for a Martian. a. Graph the situation First, we need to convert all heights to inches 4’10” = 4(12) +10 = 58” 5’1” = 5(12) + 1 =
  39. 39. Example 3 The lightest recommended weight for a Martian with height 4’10” is 109 lbs. This weight increases 2 lbs/in to a height of 5’1” and then goes up 3 lbs/in to a height of 6’ which is tall for a Martian. a. Graph the situation First, we need to convert all heights to inches 4’10” = 4(12) +10 = 58” 5’1” = 5(12) + 1 = 61”
  40. 40. Example 3 The lightest recommended weight for a Martian with height 4’10” is 109 lbs. This weight increases 2 lbs/in to a height of 5’1” and then goes up 3 lbs/in to a height of 6’ which is tall for a Martian. a. Graph the situation First, we need to convert all heights to inches 4’10” = 4(12) +10 = 58” 5’1” = 5(12) + 1 = 61” 6’ = 6(12) = 72”
  41. 41. Example 3 The lightest recommended weight for a Martian with height 4’10” is 109 lbs. This weight increases 2 lbs/in to a height of 5’1” and then goes up 3 lbs/in to a height of 6’ which is tall for a Martian. a. Graph the situation First, we need to convert all heights to inches 4’10” = 4(12) +10 = 58” 5’1” = 5(12) + 1 = 61” 6’ = 6(12) = 72” (58”, 109 lbs)
  42. 42. Example 3 The lightest recommended weight for a Martian with height 4’10” is 109 lbs. This weight increases 2 lbs/in to a height of 5’1” and then goes up 3 lbs/in to a height of 6’ which is tall for a Martian. a. Graph the situation First, we need to convert all heights to inches 4’10” = 4(12) +10 = 58” 5’1” = 5(12) + 1 = 61” 6’ = 6(12) = 72” (58”, 109 lbs) (61”, 115 lbs)
  43. 43. Example 3 The lightest recommended weight for a Martian with height 4’10” is 109 lbs. This weight increases 2 lbs/in to a height of 5’1” and then goes up 3 lbs/in to a height of 6’ which is tall for a Martian. a. Graph the situation First, we need to convert all heights to inches 4’10” = 4(12) +10 = 58” 5’1” = 5(12) + 1 = 61” 6’ = 6(12) = 72” (58”, 109 lbs) (61”, 115 lbs) (72”, 148 lbs)
  44. 44. Example 3 (con’t) (58”, 109 lbs) (61”, 115 lbs) (72”, 148 lbs) b. Find two equations that describe these situations
  45. 45. Example 3 (con’t) (58”, 109 lbs) (61”, 115 lbs) (72”, 148 lbs) b. Find two equations that describe these situations y - y1 = m(x - x1)
  46. 46. Example 3 (con’t) (58”, 109 lbs) (61”, 115 lbs) (72”, 148 lbs) b. Find two equations that describe these situations y - y1 = m(x - x1) w - w1 = m(h - h1)
  47. 47. Example 3 (con’t) (58”, 109 lbs) (61”, 115 lbs) (72”, 148 lbs) b. Find two equations that describe these situations y - y1 = m(x - x1) w - w1 = m(h - h1) w - 109 = 2(h - 58)
  48. 48. Example 3 (con’t) (58”, 109 lbs) (61”, 115 lbs) (72”, 148 lbs) b. Find two equations that describe these situations y - y1 = m(x - x1) w - w1 = m(h - h1) w - 109 = 2(h - 58) w = 2h - 7
  49. 49. Example 3 (con’t) (58”, 109 lbs) (61”, 115 lbs) (72”, 148 lbs) b. Find two equations that describe these situations y - y1 = m(x - x1) w - w1 = m(h - h1) w - 109 = 2(h - 58) w = 2h - 7 for 58 ≤ h ≤ 61
  50. 50. Example 3 (con’t) (58”, 109 lbs) (61”, 115 lbs) (72”, 148 lbs) b. Find two equations that describe these situations y - y1 = m(x - x1) w - w1 = m(h - h1) w - w1 = m(h - h1) w - 109 = 2(h - 58) w = 2h - 7 for 58 ≤ h ≤ 61
  51. 51. Example 3 (con’t) (58”, 109 lbs) (61”, 115 lbs) (72”, 148 lbs) b. Find two equations that describe these situations y - y1 = m(x - x1) w - w1 = m(h - h1) w - w1 = m(h - h1) w - 109 = 2(h - 58) w - 115 = 3(h - 61) w = 2h - 7 for 58 ≤ h ≤ 61
  52. 52. Example 3 (con’t) (58”, 109 lbs) (61”, 115 lbs) (72”, 148 lbs) b. Find two equations that describe these situations y - y1 = m(x - x1) w - w1 = m(h - h1) w - w1 = m(h - h1) w - 109 = 2(h - 58) w - 115 = 3(h - 61) w = 2h - 7 w = 3h - 68 for 58 ≤ h ≤ 61
  53. 53. Example 3 (con’t) (58”, 109 lbs) (61”, 115 lbs) (72”, 148 lbs) b. Find two equations that describe these situations y - y1 = m(x - x1) w - w1 = m(h - h1) w - w1 = m(h - h1) w - 109 = 2(h - 58) w - 115 = 3(h - 61) w = 2h - 7 w = 3h - 68 for 58 ≤ h ≤ 61 for 61 < h ≤ 72
  54. 54. Homework
  55. 55. Homework p. 165 #1 - 21 “ I’m not sure I want popular opinion on my side -- I’ve noticed those with the most opinions often have the fewest facts.” - Bethania McKenstry

×