1. SECTION 3-4
Equations of Lines
Tuesday, January 3, 2012
2. ESSENTIAL QUESTIONS
How do you write an equation of a line given
information about the graph?
How do you solve problems by writing equations?
Tuesday, January 3, 2012
4. VOCABULARY
1. Slope-intercept Form: y = mx + b, where m = slope
and b = y coordinate of the y-intercept -- (0, b)
2. Point-slope form:
Tuesday, January 3, 2012
5. VOCABULARY
1. Slope-intercept Form: y = mx + b, where m = slope
and b = y coordinate of the y-intercept -- (0, b)
2. Point-slope form: y - y1 = m(x - x1), where m = slope
and (x1, y1) is a point on the line
Tuesday, January 3, 2012
6. EXAMPLE 1
Identify the slope and y-intercept for each line and
graph the lines.
1
a. y = x
2
Tuesday, January 3, 2012
7. EXAMPLE 1
Identify the slope and y-intercept for each line and
graph the lines.
1
a. y = x
2
1
m=
2
Tuesday, January 3, 2012
8. 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
Tuesday, January 3, 2012
9. 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)
Tuesday, January 3, 2012
10. 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)
Tuesday, January 3, 2012
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
y-intercept: (0, 0)
Tuesday, January 3, 2012
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)
Tuesday, January 3, 2012
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)
Tuesday, January 3, 2012
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)
Tuesday, January 3, 2012
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)
Tuesday, January 3, 2012
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)
Tuesday, January 3, 2012
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)
Tuesday, January 3, 2012
18. EXAMPLE 1
Identify the slope and y-intercept for each line and
graph the lines.
b. 2y − x = −6
Tuesday, January 3, 2012
19. EXAMPLE 1
Identify the slope and y-intercept for each line and
graph the lines.
b. 2y − x = −6
+x
Tuesday, January 3, 2012
20. EXAMPLE 1
Identify the slope and y-intercept for each line and
graph the lines.
b. 2y − x = −6
+x +x
Tuesday, January 3, 2012
21. EXAMPLE 1
Identify the slope and y-intercept for each line and
graph the lines.
b. 2y − x = −6
+x +x
Tuesday, January 3, 2012
22. EXAMPLE 1
Identify the slope and y-intercept for each line and
graph the lines.
b. 2y − x = −6
+x +x
2y = x − 6
Tuesday, January 3, 2012
23. 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
Tuesday, January 3, 2012
24. 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
Tuesday, January 3, 2012
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
2 2
1
y = x −3
2
1
m=
2
Tuesday, January 3, 2012
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
1
y = x −3
2
1
m= y-intercept = (0, -3)
2
Tuesday, January 3, 2012
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
1
m= y-intercept = (0, -3)
2
Tuesday, January 3, 2012
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= y-intercept = (0, -3)
2
Tuesday, January 3, 2012
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
Tuesday, January 3, 2012
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
Tuesday, January 3, 2012
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
Tuesday, January 3, 2012
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
Tuesday, January 3, 2012
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
Tuesday, January 3, 2012
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
Tuesday, January 3, 2012
35. 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)
Tuesday, January 3, 2012
36. 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
Tuesday, January 3, 2012
37. 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
Tuesday, January 3, 2012
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)
Use slope-intercept
y = mx + b
y = −2x + 4
Tuesday, January 3, 2012
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
y = mx + b
y = −2x + 4
Tuesday, January 3, 2012
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
y = −2x + 4
Tuesday, January 3, 2012
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
Tuesday, January 3, 2012
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
Tuesday, January 3, 2012
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
Tuesday, January 3, 2012
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
Tuesday, January 3, 2012
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
Tuesday, January 3, 2012
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
Tuesday, January 3, 2012
47. 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)
Tuesday, January 3, 2012
48. 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
Tuesday, January 3, 2012
49. 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 )
Tuesday, January 3, 2012
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)
Use point-slope
y − y1 = m(x − x1 )
y + 2 = (x − 8)
3
4
Tuesday, January 3, 2012
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
y − y1 = m(x − x1 )
y + 2 = (x − 8) 3
4
y +2= x−6 3
4
Tuesday, January 3, 2012
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 )
y + 2 = (x − 8) 3
4
y +2= x−6 3
4
y = x−8
3
4
Tuesday, January 3, 2012
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 )
y + 2 = (x − 8) 3
4
y +2= x−6 3
4
y = x−8
3
4
Tuesday, January 3, 2012
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 )
y + 2 = (x − 8) 3
4
y +2= x−6 3
4
y = x−8
3
4
Tuesday, January 3, 2012
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 )
y + 2 = (x − 8) 3
4
y +2= x−6 3
4
y = x−8
3
4
Tuesday, January 3, 2012
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 )
y + 2 = (x − 8) 3
4
y +2= x−6 3
4
y = x−8
3
4
Tuesday, January 3, 2012
57. EXAMPLE 3
Write the equation for the line.
a.
Tuesday, January 3, 2012
58. EXAMPLE 3
Write the equation for the line.
a.
5
m=−
7
Tuesday, January 3, 2012
59. EXAMPLE 3
Write the equation for the line.
a.
5
m=− (4, -1)
7
Tuesday, January 3, 2012
60. EXAMPLE 3
Write the equation for the line.
a. y − y1 = m(x − x1 )
5
m=− (4, -1)
7
Tuesday, January 3, 2012
61. EXAMPLE 3
Write the equation for the line.
a. y − y1 = m(x − x1 )
y +1= − (x − 4)
5
7
5
m=− (4, -1)
7
Tuesday, January 3, 2012
62. EXAMPLE 3
Write the equation for the line.
a. y − y1 = m(x − x1 )
y +1= − (x − 4)
5
7
y +1= − x +
5
7
20
7
5
m=− (4, -1)
7
Tuesday, January 3, 2012
63. EXAMPLE 3
Write the equation for the line.
a. y − y1 = m(x − x1 )
y +1= − (x − 4)
5
7
y +1= − x + 5
7
20
7
5 y=− x+ 5
7
13
7
m=− (4, -1)
7
Tuesday, January 3, 2012
64. EXAMPLE 3
Write the equation for the line.
b.
Tuesday, January 3, 2012
65. EXAMPLE 3
Write the equation for the line.
b.
6
m=
8
Tuesday, January 3, 2012
66. EXAMPLE 3
Write the equation for the line.
b.
6 3
m= =
8 4
Tuesday, January 3, 2012
67. EXAMPLE 3
Write the equation for the line.
b.
6 3
m= = (3, 2)
8 4
Tuesday, January 3, 2012
68. EXAMPLE 3
Write the equation for the line.
b.
y − y1 = m(x − x1 )
6 3
m= = (3, 2)
8 4
Tuesday, January 3, 2012
69. EXAMPLE 3
Write the equation for the line.
b.
y − y1 = m(x − x1 )
y − 2 = (x − 3)
3
4
6 3
m= = (3, 2)
8 4
Tuesday, January 3, 2012
70. EXAMPLE 3
Write the equation for the line.
b.
y − y1 = m(x − x1 )
y − 2 = (x − 3)
3
4
y−2= x− 3
4
9
4
6 3
m= = (3, 2)
8 4
Tuesday, January 3, 2012
71. EXAMPLE 3
Write the equation for the line.
b.
y − y1 = m(x − x1 )
y − 2 = (x − 3)
3
4
y−2= x− 3
4
9
4
6 3 y= x−
3
4
1
4
m= = (3, 2)
8 4
Tuesday, January 3, 2012
72. CHECK YOUR
UNDERSTANDING
Review problems #1-12 on p. 200
Tuesday, January 3, 2012
74. PROBLEM SET
p. 200 #13-41 odd, 55
“We can have facts without thinking, but we cannot
have thinking without facts.” - John Dewey
Tuesday, January 3, 2012
