Embed Size (px)
Citation preview
SECTION 1.2 Lines
MATH 1310 College Algebra 27
Section 1.2: Lines
� Slope of a Line � Equation of a Line � Intercepts of Lines � Parallel and Perpendicular Lines
Slope of a Line
CHAPTER 1 An Introduction to Graphs and Lines
University of Houston Department of Mathematics 28
Solution:
SECTION 1.2 Lines
MATH 1310 College Algebra 29
CHAPTER 1 An Introduction to Graphs and Lines
University of Houston Department of Mathematics 30
Additional Example 1:
Solution:
Additional Example 2:
Solution:
SECTION 1.2 Lines
MATH 1310 College Algebra 31
Additional Example 3:
Solution:
Additional Example 4:
CHAPTER 1 An Introduction to Graphs and Lines
University of Houston Department of Mathematics 32
Solution:
SECTION 1.2 Lines
MATH 1310 College Algebra 33
Equation of a Line
Solution:
CHAPTER 1 An Introduction to Graphs and Lines
University of Houston Department of Mathematics 34
Solution:
SECTION 1.2 Lines
MATH 1310 College Algebra 35
Solution:
Solution:
CHAPTER 1 An Introduction to Graphs and Lines
University of Houston Department of Mathematics 36
Additional Example 1:
Solution:
SECTION 1.2 Lines
MATH 1310 College Algebra 37
Additional Example 2:
Solution:
CHAPTER 1 An Introduction to Graphs and Lines
University of Houston Department of Mathematics 38
Additional Example 3:
Solution:
SECTION 1.2 Lines
MATH 1310 College Algebra 39
Additional Example 4:
Solution:
CHAPTER 1 An Introduction to Graphs and Lines
University of Houston Department of Mathematics 40
Intercepts of Lines
SECTION 1.2 Lines
MATH 1310 College Algebra 41
CHAPTER 1 An Introduction to Graphs and Lines
University of Houston Department of Mathematics 42
Solution:
SECTION 1.2 Lines
MATH 1310 College Algebra 43
Solution:
CHAPTER 1 An Introduction to Graphs and Lines
University of Houston Department of Mathematics 44
Additional Example 1:
Solution:
SECTION 1.2 Lines
MATH 1310 College Algebra 45
Additional Example 2:
Solution:
CHAPTER 1 An Introduction to Graphs and Lines
University of Houston Department of Mathematics 46
Additional Example 3:
Solution:
SECTION 1.2 Lines
MATH 1310 College Algebra 47
Parallel and Perpendicular Lines
CHAPTER 1 An Introduction to Graphs and Lines
University of Houston Department of Mathematics 48
Solution:
SECTION 1.2 Lines
MATH 1310 College Algebra 49
Solution:
CHAPTER 1 An Introduction to Graphs and Lines
University of Houston Department of Mathematics 50
Additional Example 1:
Solution:
Additional Example 2:
Solution:
SECTION 1.2 Lines
MATH 1310 College Algebra 51
Additional Example 3:
Solution:
Additional Example 4:
Solution:
CHAPTER 1 An Introduction to Graphs and Lines
University of Houston Department of Mathematics 52
Exercise Set 1.2: Lines
MATH 1310 College Algebra 53
−4 −2 2 4
−6
−4
−2
2
x
y
−6 −4 −2 2
−6
−4
−2
x
y
−4 −2 2 4
−4
−2
2
4
x
y
−2 2 4
−2
2
4
x
y
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
Find the slope of the line that passes through the
following points. If it is undefined, state ‘undefined.’
7. )7,3( and )0,0(
8. )5,3( and )0,8(
9. )10,4( and )5,2(
10. )9,5( and )3,7(
11. )7,6( and )3,2( −−
12. )10,5( and )6,1( −−−
13. )4,3( and )8,3( −−
14. )7,1( and )7,8( −−−
Find the slope of each of the following lines.
15. c
16. d
17. e
18. f
Write an equation for each of the following lines.
19.
20.
21.
22.
−8 −6 −4 −2 2 4 6 8
−10
−8
−6
−4
−2
2
4
6
8
x
y
p
q
r
t
s
w
−5 −4 −3 −2 −1 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
x
ye
c
c
f
d
Exercise Set 1.2: Lines
University of Houston Department of Mathematics 54
Write each of the following equations in slope-
intercept form, identify the slope and y-intercept, and
then draw its graph.
23. 52 =+ yx
24. 63 −=− yx
25. 04 =+ yx
26. 1052 =+ yx
27. 0934 =+− yx
28. 121
32 −=+− yx
Write an equation of the line that satisfies the given
conditions.
29. Slope 7
4- ; y-intercept 3
30. Slope 4− ; y-intercept 5
31. Slope 3
2; passes through (-6 4)
32. Slope 2
5− ; passes through (8, -3)
33. Slope 9
2− ; passes through (-3, 2)
34. Slope 5
1; passes through (-4, -2)
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 2
3− ; x-intercept 4
42. Slope 5
1; x-intercept -6
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 4=x
46. Passes through (2, -6); parallel to the line
4=y
47. Passes through (5, -7); parallel to the line 35 +−= xy
48. Passes through (5, -7); perpendicular to the line
35 +−= xy
49. Passes through (2, 3); parallel to the line
625 =− yx
50. Passes through (-1, 5); parallel to the line
834 =+ yx
51. Passes through (2, 3); perpendicular to the line
625 =− yx
52. Passes through (-1, 5); perpendicular to the line
834 =+ yx
53. Passes through (4, -6); parallel to the line
containing (3, -5) and (2, 1)
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 32 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.
