Upcoming SlideShare
×

# Integrated 2 Section 6-3

652 views

Published on

Write and Graph Equations

Published in: Education, Technology
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
652
On SlideShare
0
From Embeds
0
Number of Embeds
14
Actions
Shares
0
12
0
Likes
0
Embeds 0
No embeds

No notes for slide
• ### Integrated 2 Section 6-3

1. 1. SECTION 6-3 Write and Graph Equations
2. 2. ESSENTIAL QUESTIONS How do you write equations of lines using slope, intercepts, and points? How do you graph a line given the equation? Where you’ll see this: Finance, sports, transportation, recreation
3. 3. VOCABULARY 1. Linear Equation: 2. y-intercept: 3. Slope-intercept Form: 4. Point-slope form:
4. 4. VOCABULARY 1. Linear Equation: An equation whose graph is a line 2. y-intercept: 3. Slope-intercept Form: 4. Point-slope form:
5. 5. VOCABULARY 1. Linear Equation: An equation whose graph is a line 2. y-intercept: The point where the graph crosses the y-axis 3. Slope-intercept Form: 4. Point-slope form:
6. 6. VOCABULARY 1. Linear Equation: An equation whose graph is a line 2. y-intercept: The point where the graph crosses the y-axis (It’s a point!) 3. Slope-intercept Form: 4. Point-slope form:
7. 7. VOCABULARY 1. Linear Equation: An equation whose graph is a line 2. y-intercept: The point where the graph crosses the y-axis (It’s a point!) 3. Slope-intercept Form: y = mx + b, where m = slope and b = y coordinate of the y-intercept 4. Point-slope form:
8. 8. VOCABULARY 1. Linear Equation: An equation whose graph is a line 2. y-intercept: The point where the graph crosses the y-axis (It’s a point!) 3. Slope-intercept Form: y = mx + b, where m = slope and b = y coordinate of the y-intercept 4. Point-slope form: y - y1 = m(x - x1), where m = slope and (x1, y1) is a point on the line
9. 9. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2
10. 10. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2 1 m= 2
11. 11. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2 1 m= 2 b=0
12. 12. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2 1 m= 2 b=0 y-intercept: (0, 0)
13. 13. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2 1 m= 2 b=0 y-intercept: (0, 0)
14. 14. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2 1 m= 2 b=0 y-intercept: (0, 0)
15. 15. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2 1 m= 2 b=0 y-intercept: (0, 0)
16. 16. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2 1 m= 2 b=0 y-intercept: (0, 0)
17. 17. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2 1 m= 2 b=0 y-intercept: (0, 0)
18. 18. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2 1 m= 2 b=0 y-intercept: (0, 0)
19. 19. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2 1 m= 2 b=0 y-intercept: (0, 0)
20. 20. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2 1 m= 2 b=0 y-intercept: (0, 0)
21. 21. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6
22. 22. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x
23. 23. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x
24. 24. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x
25. 25. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6
26. 26. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2
27. 27. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2 1 y = x −3 2
28. 28. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2 1 y = x −3 2 1 m= 2
29. 29. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2 1 y = x −3 2 1 m= y-intercept = (0, -3) 2
30. 30. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2 1 y = x −3 2 1 m= y-intercept = (0, -3) 2
31. 31. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2 1 y = x −3 2 1 m= y-intercept = (0, -3) 2
32. 32. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2 1 y = x −3 2 1 m= y-intercept = (0, -3) 2
33. 33. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2 1 y = x −3 2 1 m= y-intercept = (0, -3) 2
34. 34. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2 1 y = x −3 2 1 m= y-intercept = (0, -3) 2
35. 35. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2 1 y = x −3 2 1 m= y-intercept = (0, -3) 2
36. 36. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2 1 y = x −3 2 1 m= y-intercept = (0, -3) 2
37. 37. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2 1 y = x −3 2 1 m= y-intercept = (0, -3) 2
38. 38. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4)
39. 39. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4) Use slope-intercept
40. 40. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4) Use slope-intercept y = mx + b
41. 41. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4) Use slope-intercept y = mx + b y = −2x + 4
42. 42. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4) Use slope-intercept y = mx + b y = −2x + 4
43. 43. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4) Use slope-intercept y = mx + b y = −2x + 4
44. 44. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4) Use slope-intercept y = mx + b y = −2x + 4
45. 45. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4) Use slope-intercept y = mx + b y = −2x + 4
46. 46. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4) Use slope-intercept y = mx + b y = −2x + 4
47. 47. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4) Use slope-intercept y = mx + b y = −2x + 4
48. 48. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4) Use slope-intercept y = mx + b y = −2x + 4
49. 49. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4) Use slope-intercept y = mx + b y = −2x + 4
50. 50. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. b. m = 3/4, (8, -2)
51. 51. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. b. m = 3/4, (8, -2) Use point-slope
52. 52. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. b. m = 3/4, (8, -2) Use point-slope y − y1 = m(x − x1 )
53. 53. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. b. m = 3/4, (8, -2) Use point-slope y − y1 = m(x − x1 ) 3 y + 2 = (x − 8) 4
54. 54. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. b. m = 3/4, (8, -2) Use point-slope y − y1 = m(x − x1 ) 3 y + 2 = (x − 8) 4 3 y +2= x−6 4
55. 55. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. b. m = 3/4, (8, -2) Use point-slope y − y1 = m(x − x1 ) 3 y + 2 = (x − 8) 4 3 3 y +2= x−6 4 y = x−8 4
56. 56. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. b. m = 3/4, (8, -2) Use point-slope y − y1 = m(x − x1 ) 3 y + 2 = (x − 8) 4 3 3 y +2= x−6 4 y = x−8 4
57. 57. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. b. m = 3/4, (8, -2) Use point-slope y − y1 = m(x − x1 ) 3 y + 2 = (x − 8) 4 3 3 y +2= x−6 4 y = x−8 4
58. 58. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. b. m = 3/4, (8, -2) Use point-slope y − y1 = m(x − x1 ) 3 y + 2 = (x − 8) 4 3 3 y +2= x−6 4 y = x−8 4
59. 59. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. b. m = 3/4, (8, -2) Use point-slope y − y1 = m(x − x1 ) 3 y + 2 = (x − 8) 4 3 3 y +2= x−6 4 y = x−8 4
60. 60. EXAMPLE 3 Write the equation for the line. a.
61. 61. EXAMPLE 3 Write the equation for the line. a. 5 m=− 7
62. 62. EXAMPLE 3 Write the equation for the line. a. 5 m=− (4, -1) 7
63. 63. EXAMPLE 3 Write the equation for the line. a. y − y1 = m(x − x1 ) 5 m=− (4, -1) 7
64. 64. EXAMPLE 3 Write the equation for the line. a. y − y1 = m(x − x1 ) 5 y +1= − (x − 4) 7 5 m=− (4, -1) 7
65. 65. EXAMPLE 3 Write the equation for the line. a. y − y1 = m(x − x1 ) 5 y +1= − (x − 4) 7 5 20 y +1= − x + 7 7 5 m=− (4, -1) 7
66. 66. EXAMPLE 3 Write the equation for the line. a. y − y1 = m(x − x1 ) 5 y +1= − (x − 4) 7 5 20 y +1= − x + 7 7 5 13 5 y=− x+ 7 7 m=− (4, -1) 7
67. 67. EXAMPLE 3 Write the equation for the line. b.
68. 68. EXAMPLE 3 Write the equation for the line. b. 6 m= 8
69. 69. EXAMPLE 3 Write the equation for the line. b. 6 3 m= = 8 4
70. 70. EXAMPLE 3 Write the equation for the line. b. 6 3 m= = (3, 2) 8 4
71. 71. EXAMPLE 3 Write the equation for the line. b. y − y1 = m(x − x1 ) 6 3 m= = (3, 2) 8 4
72. 72. EXAMPLE 3 Write the equation for the line. b. y − y1 = m(x − x1 ) 3 y − 2 = (x − 3) 4 6 3 m= = (3, 2) 8 4
73. 73. EXAMPLE 3 Write the equation for the line. b. y − y1 = m(x − x1 ) 3 y − 2 = (x − 3) 4 3 9 y−2= x− 4 4 6 3 m= = (3, 2) 8 4
74. 74. EXAMPLE 3 Write the equation for the line. b. y − y1 = m(x − x1 ) 3 y − 2 = (x − 3) 4 3 9 y−2= x− 4 4 3 1 6 3 y= x− 4 4 m= = (3, 2) 8 4
75. 75. HOMEWORK
76. 76. HOMEWORK p. 256 #1-33 odd, 34 “We can have facts without thinking, but we cannot have thinking without facts.” - John Dewey