Download Chapter 4.2 Answers - Aspen High School - Algebra I

3 APPLY
ASSIGNMENT GUIDE
BASIC
Day 1: pp. 214–215 Exs. 12–35,
36–50 even
Day 2: pp. 215–217 Exs. 52–55,
60–70, 74–78, 85, 90, 95
GUIDED PRACTICE
Vocabulary Check
✓
Concept Check
✓
Skill Check
ADVANCED
Day 1: pp. 214–215 Exs. 12–35,
36–50 even
Day 2: pp. 215–217 Exs. 52–56,
60–66, 71–80, 85, 90, 95
BLOCK SCHEDULE
pp. 214–217 Exs. 12–35,
36–50 even, 52–55, 60–70,
74–78, 85, 90, 95
EXERCISE LEVELS
Level A: Easier
12–20, 81–94
Level B: More Difficult
21–55, 57, 58, 60–66, 74–78, 95–98
Level C: Most Difficult
56, 59, 67–73, 79, 80
HOMEWORK CHECK
To quickly check student understanding of key concepts, go
over the following exercises:
Exs. 12, 16, 18, 22, 32, 38, 60, 68.
See also the Daily Homework Quiz:
• Blackline Master (Chapter 4
Resource Book, p. 38)
•
Transparency (p. 30)
4.
y
1
1
1
3
1
3
x
✓
2. Yes; for every value of
x, you will solve the
equation to find the
appropriate value for y
so that (x, y) is on the
line.
equation x = 3 is a horizontal line. Explain.
False; the graph of x = 3 is a vertical line.
Use a table of values to graph the equation. 4–6. See margin.
5. x = 1.5
4. 6x º 3y = 12
6. y = º2
Tell whether the point is a solution of the equation 4x º y = 1.
7. (º1, 3) no
11.
8. (1, 3) yes
9. (1, 0) no
10. (1, 4) no
INTERNET ACCESS Using the graph or the model in Example 4,
estimate the number of households that had Internet access in 1999.
about 35,180,000 households
PRACTICE AND APPLICATIONS
STUDENT HELP
Extra Practice
to help you master
skills is on p. 800.
12 a. yes; 3(2) º 4(º1) = 10
b. no; 3(º1) º 4(2) =
º11 ≠ 10
VERIFYING SOLUTIONS Use the graph to decide whether the point lies on
the graph of the line. Justify your answer algebraically.
13. y = 5
12. 3x º 4y = 10
See margin.
a. (2, º1)
b. (º1, 2)
14. x = 0
a. (5, 0) no; y ≠ 5
a. (0, 14) yes; x = 0
b. (0, 5) yes; y = 5
b. (14, 0)
no; x ≠ 0
y
y
y
3
1
1
1
1
4 x
22. (º1, 11), (0, 7), (1, 3)
冉 12 冊 冉 12 冊 冉 12 冊
25. } }, º1 , }}, 0 , }}, 1
26.(º1, º6), (0, º6), (1, º6)
3
1
1
1
1
1
24. (2, º1), (2, 0), (2, 1)
1
3 x
1
3 x
CHECKING SOLUTIONS Decide whether the given ordered pair is a solution
of the equation.
15. 2y º 4x = 8, (º2, 8) no
16. º5x º 8y = 15, (º3, 0) yes
STUDENT HELP
17. y = º2, (º2, º2) yes
18. x = º4, (1, º4) no
HOMEWORK HELP
19. 6y º 3x = º9, (2, º1) no
20. º2x º 9y = 7, (º1, º1) no
Example 1:
Example 2:
Example 3:
Example 4:
Example 5:
Exs. 12–20
Exs. 21–55
Exs. 21–55
Exs. 67–70
Exs. 44–55,
60–65
Example 6: Exs. 44–55,
60–65
6x 3y 12
214
214
2. In Example 2, if you choose a value of x different from those in the table of
values, will you find a solution that lies on the same line? Explain. See margin.
3. Decide whether the following statement is true or false. The graph of the
AVERAGE
Day 1: pp. 214–215 Exs. 12–35,
36–50 even
Day 2: pp. 215–217 Exs. 52–55,
60–70, 74–78, 85, 90, 95
1. Complete the following sentence: An ordered pair that makes an equation in
? . solution of the equation
two variables true is called a(n) 㛭㛭㛭
FINDING SOLUTIONS Find three different ordered pairs that are solutions
of the equation. 21–29. Sample answers are given.
21. y = 3x º 5
(º1, º8), (0, º5), (1, º2)
24. x = 2 See margin.
1
27. y = (4 º 2x)
2
(º1, 3), (0, 2), (1, 1)
22. y = 7 º 4x See margin. 23. y = º2x º 6
(º1, º4), (0, º6), (1, º8)
1
25. x = See margin.
26. y = º6 See margin.
2
1
28. y = 3(6x º 1)
29. y = 4 x º 1
2
(º1, º6), (0, º4), (1, º2)
(º1, º21), (0, º3), (1, 15)
Chapter 4 Graphing Linear Equations and Functions
冉
冊
2
3
1
32. y = º}}x + 12
4
19
33. y = ºx + }}
5
2
1
34. y = º}}x + }}
5
5
31. y = º}}x + 2
FUNCTION FORM Rewrite the equation in function form.
30. º3x + y = 12
31. 2x + 3y = 6
32. x + 4y = 48
See margin.
y = 3x + 12
See margin.
1
5
33. 5x + 5y = 19
34. x + y = 1
35. ºx º y = 5
2
2
y = ºx º 5
See margin.
See margin.
GRAPHING EQUATIONS Use a table of values to graph the equation.
36–51. See margin.
36. y = ºx + 4
37. y = º2x + 5
38. y = º(3 º x) 39. y = º2(x º 6)
40. y = 3x + 2
41. y = 4x º 1
4
42. y = x + 2
3
3
43. y = ºx + 1
4
44. x = 9
45. y = º1
46. y = 0
47. y = º3x + 1
48. x = 0
49. x º 2y = 6
50. 4x + 4y = 2
51. x + 2y = º8
MATCHING EQUATIONS WITH GRAPHS Match the equation with its graph.
A. x = º2
B. 2x º y = 3
C. 6x + 3y = 0
D. ºx + 2y = 6
y
52.
B
1
1
1
3 x
Look Back When students look
back to p. 204, remind them
that the x-coordinates should
be entered in List 1 and the
y-coordinates should be entered
in List 2 in the STAT EDIT menu.
GRAPHING CALCULATOR
NOTE
EXERCISES 57–58 The graphing calculator will be used to graph
decimal values and introduce students to the notion of a line of fit for
a set of data.
5.
y
53.
STUDENT HELP NOTES
y
3
D
1
1
1
1
3
1
1
1
y
A
55.
y
1
1
3
1
1
y
3
C
2
3
1 x
1
1
1
1
1
3 x
3
36.
56. CRITICAL THINKING Robin always finds at least three different ordered pairs
when making a table to graph an equation. Why do you think she does this?
STUDENT HELP
Look Back
For help with scatter
plots, see p. 204.
x
x 1.5
3
x
6.
54.
3
as a check
PLOTTING POINTS In Exercises 57º59, use the ordered pairs below.
1
3 x
y 2
y
3
y x 4
1
1
1
(º3, º9), (º2, º7), (º1.6, º5.5), (0.4, º2.2), (3.1, 3.2), (5.2, 7.4)
57. Use a graphing calculator or a computer to graph the ordered pairs.
See margin.
58. The line that fits most of the points is the graph of y = 2x º 3. One of the
1
3
x
37–51, 57. See Additional Answers
beginning on page AA1.
points does not appear to fall on the line with the others. Which point is it?
(º1.6, º5.5)
59. Show algebraically that one point does not lie on this line.
x = º1.6; 2(º1.6) º 3 = º6.2, but y = º5.5.
POINTS OF INTERSECTION In Exercises 60–65, graph the two lines in the
same coordinate plane. Then find the coordinates of the point at which
the lines cross. 60–65. Check graphs.
60. x = º5, y = 2 (º5, 2) 61. y = 11, x = º8 (º8, 11) 62. y = º6, x = 1 (1, º6)
63. x = 4, y = º4 (4, º4) 64. y = º1, x = 0 (0, º1) 65. x = 3, y = 0 (3, 0)
66. VISUAL THINKING Name a point that would be on the graphs of both
x = º3 and y = 2. Sketch both graphs to verify your answer. (º3, 2); Check
graphs.
4.2 Graphing Linear Equations
215
215
72.
and $10 to trim bushes. You want to make
$300 in one week. An algebraic model for
your earnings is 20x + 10y = 300, where x
is the number of lawns you mow and y is the
number of bushes you trim.
67. Solve the equation for y. y = º2x + 30
68.
5
y = º2x + 30
20
10
10
15
0
x
Minutes swimming
y
40
0
0
x
40
80
Minutes running
68. Use the equation in function form from
71. Running time; Calories
burned while swimming;
7.1; Calories burned
while swimming;
Swimming time;
7.1x + 10.1y = 800
Exercise 67 to make a table of values for
x = 5, x = 10, and x = 15.
69. Look at the graph at the right. Does the
line shown appear to pass through the points
from your table of values? yes
TRAINING FOR A TRIATHLON In Exercises 71º73, Mary Gordon is
training for a triathlon. Like most triathletes she regularly trains in two
of the three events every day. On Saturdays she expects to burn about
800 calories during her workout by running and swimming.
Running:
7.1 calories per minute
Swimming:
10.1 calories per minute
Bicycling:
6.2 calories per minute
minutes she spends running, and let y represent the number of minutes she
spends swimming. See margin.
FOCUS ON
APPLICATIONS
VERBAL
MODEL
LABELS
Calories burned
Swimming
Total calories
? + ? •
=
while running •
Time
burned
Calories burned while running = ?
Running time = x
? = 10.1
? = y
Total calories burned = 800
ADDITIONAL PRACTICE
AND RETEACHING
For more Mixed Review:
•
Search the Test and Practice
Generator for key words or
specific lessons.
216
RE
L
AL I
FE
TRIATHLON
In 1998, over 1500
people competed in Hawaii’s
Ironman Triathlon World
Championship.
INT
• Practice Levels A, B, and C
(Chapter 4 Resource Book, p. 28)
• Reteaching with Practice
(Chapter 4 Resource Book, p. 31)
•
See Lesson 4.2 of the
Personal Student Tutor
0 5 10 15 20 x
Lawns mowed
71. Copy and complete the model below. Let x represent the number of
79. See Additional Answers beginning on page AA1.
For Lesson 4.2:
y
30
25
20
15
10
5
0
70. If you do not trim any bushes during the week, how many lawns
will you have to mow to earn $300? 15 lawns
Triathlon Training
80
Bushes trimmed
APPLICATION NOTE
EXERCISES 72–73 Students
should understand that numbers
given for calories burned per minute
are averages. The body weight and
metabolism of each triathlete are
factors affecting the number of
calories he or she will burn during
each activity. For example, a person
who weighs 140 pounds will burn
508 calories while bicycling for one
hour at about 12–13 mi/h and exerting a moderate effort. A person
weighing 195 pounds will burn
708 calories in the same activity.
Additional information about
the Ironman Triathlon World
Championship is available at
www.mcdougallittell.com.
LANDSCAPING BUSINESS In Exercises 67º70, use the following
information.
Summer Earnings
One summer you charge $20 to mow a lawn
NE
ER T
APPLICATION LINK
www.mcdougallittell.com
216
ALGEBRAIC
MODEL
? • x + ? • y = 800
(calories/minute)
(minutes)
(calories/minute)
(minutes)
(calories)
Write a linear model.
72. Make a table of values and graph the equation from Exercise 71. See margin.
73. If Mary Gordon spends 45 minutes running, about how many minutes will
she have to spend swimming to burn 800 calories? about 48 min
Chapter 4 Graphing Linear Equations and Functions
CHOOSING A MODEL In Exercises 74 and 75, decide whether a graph of the
data would be points that appear to lie on a horizontal line, a vertical line,
or neither. Explain. Let the x-axis represent time.
Test
Preparation
74. Sample answer: neither;
a vertical line makes no
sense in this situation
and a horizontal line is
unlikely since Avery
probably does not read
the same number of
books each year.
★ Challenge
74. The number of books read by Avery each year from 1999 to 2005. See margin.
DAILY HOMEWORK QUIZ
75. The number of senators in the United States Congress each year
from 1991 to 2000. Horizontal; the number of senators does not vary.
Transparency Available
1. Decide whether the given
ordered pair is a solution of
2x – 3y = 8.
a. (–2, –4) yes
b. (7, –2) no
2. Rewrite 4x – 2y = 18 in function
form. y = 2x – 9
3. Use a table of values to graph
y = 2x + 2.
76. MULTIPLE CHOICE Which point lies on the graph of 2x + 5y = 6? D
A
¡
(º2, 2)
B
¡
(3, 0)
C
¡
D
¡
(0, 3)
both A and B
77. MULTIPLE CHOICE Which point does not lie on the graph of y = 3? C
A
¡
(0, 3)
B
¡
(º3, 3)
C
¡
1
D 冢ᎏᎏ, 3冣
¡
3
(3, º3)
?. A
78. MULTIPLE CHOICE The ordered pair (º3, 5) is a solution of 㛭㛭㛭
A
¡
y=5
B
¡
x=5
C
¡
1
2
y = ᎏᎏx º 2
D
¡
1
2
y = ºᎏᎏx º 2
MISINTERPRETING GRAPHS Even though they provide an accurate
representation of data, some graphs are easy to misinterpret. In Exercises
79 and 80, use the following.
80. CRITICAL THINKING What are the advantages and disadvantages of each
graph? Sample answer: The first graph might be used to imply that profits
remained steady. (The actual decrease was about 0.030% per year.)
The second graph might be used to imply that profits decreased
steeply. The second graph is more likely to be misinterpreted.
冋
冋
冋
冋
16 3
87. º4 18
册
册
册
册
º12 0
88.
15 17
89.
º16 50
º9 19
4 º18
90. 16 º4
81. 5 + 2 + (º3) 4
º29
82. º6 + (º14) + 8 º12 83. º18 + (º10) + (º1)
1
1
84. ºᎏᎏ + 6 + ᎏᎏ 6
3
3
4
3
85. ᎏᎏ + ᎏᎏ º 1 0
7
7
MATRICES Find the sum of the matrices. (Review 2.4)
87.
89.
冋
冋
册 冋
册 冋
1 6
15 º3
+
º4 2
0 16
册
4 10
º20 40
+
º1 9
º8 10
88.
册
90.
2 5
º14 º5
+
3 10
12
7
册
册
x = 3 are all the points whose
x-coordinate is 3. The solutions of
y = –1 are all the points whose
y-coordinate is –1. The point
(3, –1) satisfies both conditions.
5 º2
º1 º16
+
5 º1
11 º3
2. OPEN ENDED Describe a
real-life situation that can be
modeled by the equation
3x + 5y = 500. See sample
SOLVING EQUATIONS Solve the equation. (Review 3.2 for 4.3)
1
91. º2z = º26 13 92. 9x = 3 }3}
93. 6p = º96 º16 94. 24 = 8c 3
p
2
95. ᎏᎏt = º10 º15 96. ºᎏᎏ = º9 63
7
3
n
3
97. ᎏᎏ = ᎏᎏ 9
15
5
c
2
98. ᎏᎏ = ᎏᎏ 4
6
3
4.2 Graphing Linear Equations
Additional Test Preparation Sample answer:
2. A store makes a $3 profit on each short-sleeve T-shirt
and a $5 profit on each long-sleeve T-shirt. If x represents the number of short-sleeve shirts sold and
Challenge problems for
Lesson 4.2 are available in
blackline format in the Chapter 4
Resource Book, p. 35 and at
www.mcdougallittell.com.
ADDITIONAL TEST
PREPARATION
1. WRITING Explain why the point
(3, –1) is a solution of both x = 3
and y = –1. The solutions of
14
}}
9
87–90. See margin.
冋 册 冋
冋 册 冋
3 x
EXTRA CHALLENGE NOTE
EVALUATING EXPRESSIONS Evaluate the expression. (Review 2.2)
7
1
86. ºᎏᎏ + ᎏᎏ + 2
9
3
1
4. Find the coordinates of the
point at which the lines cross.
a. x = –3, y = 8 (–3, 8)
b. y = 0, x = 5 (5, 0)
into $1,000,000 intervals. In the second graph start at $3,000,000 and use
$1000 intervals. See margin.
MIXED REVIEW
⫺1
⫺3
79. Sketch two graphs of the model. In the first graph, divide the vertical axis
EXTRA CHALLENGE
y
3
⫺3
Based on actual and projected data from 1995 to 2000, a linear model for a
company’s profit P is P = 3,005,000 º 900t, where t represents the number
of years since 1995.
www.mcdougallittell.com
4 ASSESS
answer at left.
217
y represents the number of long-sleeve shirts sold, then
the solutions of 3x + 5y = 500 represent the number of
each kind of T-shirt sold to make a profit of $500.
217