Download Lines - College Algebra Section 1.2

SECTION 1.2 Lines
Section 1.2:
Lines
Slope of a Line
Equation of a Line
Intercepts of Lines
Parallel and Perpendicular Lines
Slope of a Line
MATH 1310 College Algebra
27
CHAPTER 1 An Introduction to Graphs and Lines
Solution:
28
University of Houston Department of Mathematics
SECTION 1.2 Lines
MATH 1310 College Algebra
29
CHAPTER 1 An Introduction to Graphs and Lines
Additional Example 1:
Solution:
Additional Example 2:
Solution:
30
University of Houston Department of Mathematics
SECTION 1.2 Lines
Additional Example 3:
Solution:
Additional Example 4:
MATH 1310 College Algebra
31
CHAPTER 1 An Introduction to Graphs and Lines
Solution:
32
University of Houston Department of Mathematics
SECTION 1.2 Lines
Equation of a Line
Solution:
MATH 1310 College Algebra
33
CHAPTER 1 An Introduction to Graphs and Lines
Solution:
34
University of Houston Department of Mathematics
SECTION 1.2 Lines
Solution:
Solution:
MATH 1310 College Algebra
35
CHAPTER 1 An Introduction to Graphs and Lines
Additional Example 1:
Solution:
36
University of Houston Department of Mathematics
SECTION 1.2 Lines
Additional Example 2:
Solution:
MATH 1310 College Algebra
37
CHAPTER 1 An Introduction to Graphs and Lines
Additional Example 3:
Solution:
38
University of Houston Department of Mathematics
SECTION 1.2 Lines
Additional Example 4:
Solution:
MATH 1310 College Algebra
39
CHAPTER 1 An Introduction to Graphs and Lines
Intercepts of Lines
40
University of Houston Department of Mathematics
SECTION 1.2 Lines
MATH 1310 College Algebra
41
CHAPTER 1 An Introduction to Graphs and Lines
Solution:
42
University of Houston Department of Mathematics
SECTION 1.2 Lines
Solution:
MATH 1310 College Algebra
43
CHAPTER 1 An Introduction to Graphs and Lines
Additional Example 1:
Solution:
44
University of Houston Department of Mathematics
SECTION 1.2 Lines
Additional Example 2:
Solution:
MATH 1310 College Algebra
45
CHAPTER 1 An Introduction to Graphs and Lines
Additional Example 3:
Solution:
46
University of Houston Department of Mathematics
SECTION 1.2 Lines
Parallel and Perpendicular Lines
MATH 1310 College Algebra
47
CHAPTER 1 An Introduction to Graphs and Lines
Solution:
48
University of Houston Department of Mathematics
SECTION 1.2 Lines
Solution:
MATH 1310 College Algebra
49
CHAPTER 1 An Introduction to Graphs and Lines
Additional Example 1:
Solution:
Additional Example 2:
Solution:
50
University of Houston Department of Mathematics
SECTION 1.2 Lines
Additional Example 3:
Solution:
Additional Example 4:
Solution:
MATH 1310 College Algebra
51
CHAPTER 1 An Introduction to Graphs and Lines
52
University of Houston Department of Mathematics
Exercise Set 1.2: Lines
State whether the slope of each of the following lines is
positive, negative, zero, or undefined.
1.
p
2.
q
3.
r
4.
s
5.
t
6.
w
Write an equation for each of the following lines.
19.
y
q
y
8
r
2
6
x
4
−4
2
−2
2
−2
x
−8 −6 −4 −2
−2
2
4
6
8
4
−4
t
−6
−4
−6
w
−8
s
−10
p
y
20.
4
2
Find the slope of the line that passes through the
following points. If it is undefined, state ‘undefined.’
x
7.
(0, 0) and (3, 7)
8.
(8, 0) and (3, 5)
9.
(2, 5) and (4, 10)
−2
2
4
−2
10. (7, 3) and (5, 9)
y
21.
11. (−2, 3) and (6, − 7)
x
12. (−1, − 6) and (−5, 10)
−6
−4
−2
2
13. (3, − 8) and (3, − 4)
−2
14. (8, − 7) and (−1, − 7)
−4
Find the slope of each of the following lines.
15. c
e
c
−6
y
4
3
16. d
17. e
18. f
c
y
22.
4
2
1
−5 −4 −3 −2 −1
−1
x
1
2
3
4
2
5
x
−2
−4
−2
2
4
−3
f
−4
−2
−5
d
MATH 1310 College Algebra
−4
53
Exercise Set 1.2: Lines
Write each of the following equations in slopeintercept form, identify the slope and y-intercept, and
then draw its graph.
23. 2 x + y = 5
24. 3 x − y = −6
25. x + 4 y = 0
26. 2 x + 5 y = 10
27. 4 x − 3 y + 9 = 0
28. − 23 x + 12 y = −1
Write an equation of the line that satisfies the given
conditions.
29. Slope -
4
; y-intercept 3
7
47. Passes through (5, -7); parallel to the line
y = −5 x + 3
48. Passes through (5, -7); perpendicular to the line
y = −5 x + 3
49. Passes through (2, 3); parallel to the line
5x − 2 y = 6
50. Passes through (-1, 5); parallel to the line
4x + 3y = 8
51. Passes through (2, 3); perpendicular to the line
5x − 2 y = 6
52. Passes through (-1, 5); perpendicular to the line
4x + 3y = 8
53. Passes through (4, -6); parallel to the line
containing (3, -5) and (2, 1)
30. Slope − 4 ; y-intercept 5
2
31. Slope ; passes through (-6 4)
3
32. Slope −
5
; passes through (8, -3)
2
33. Slope −
2
; passes through (-3, 2)
9
34. Slope
1
; passes through (-4, -2)
5
35. Passes through (-5, 2) and (-4, -6)
36. Passes through (2, 11) and (-3, 1)
37. Passes through (-4, 5) and (1, -2)
38. Passes through (7, 0) and (3, -5)
39. x-intercept 7; y-intercept -5
40. x-intercept -2; y-intercept 6
41. Slope −
42. Slope
3
; x-intercept 4
2
1
; x-intercept -6
5
43. Passes through (1, 4); parallel to the x-axis
44. Passes through (1, 4); parallel to the y-axis
45. Passes through (2, -6); parallel to the line
x=4
46. Passes through (2, -6); parallel to the line
y=4
54
54. Perpendicular to the line containing (4, -2) and
(10, 4); passes through the midpoint of the line
segment connecting these points.
Answer the following.
55. Sketch the line with slope
2
3
that passes through
the point (3, -4), and then find its equation.
56. Determine whether or not the following points
are collinear by using the slope formula:
(a) A(-3, 4), B(3, 8), C(6, 10)
(b) D(-2, -5), E(0, -3), F(3, 1)
57. Use slopes to show that the following vertices
represent the vertices of a parallelogram:
A(-3, 4), B(0, 8), C(5, 2), D(2, -2)
58. Use slopes to show that the following vertices
represent the vertices of a rectangle:
A(-2, -3), B(1, 4), C(-6, 7), D(-9, 0)
Answer the following, assuming that each situation
can be modeled by a linear equation.
59. If a company can make 21 computers for
$23,000, and can make 40 computers for
$38,200, write an equation that represents the
cost of x computers.
60. A certain electrician charges a $40 traveling fee,
and then charges $55 per hour of labor. Write an
equation that represents the cost of a job that
takes x hours.
University of Houston Department of Mathematics