Embed Size (px)
Citation preview
Name: Date:
© M
arsh
all C
aven
dish
Inte
rnat
iona
l (Si
ngap
ore)
Priv
ate
Lim
ited.
60 Chapter 4 Lesson 4.5
Lesson 4.5 Real-World Problems: Linear Equations
Solve. Show your work.
1. To rent a bike, Max pays a flat rate plus an hourly rental fee. The graph shows the amount, C dollars, he pays based on the number of hours, t, he uses the bike.
t
5
10
15
20
25
30
21 3 5 7 94 6 8 100
C
a) Find the vertical intercept of the graph and explain what information it gives about the situation.
b) Find the slope of the graph and explain what information it gives about the situation.
c) Find the amount Max pays to rent a bike for 6 hours.
Bike Rental Rates
Time (h)
Co
st ($
)
MIF_ExtraPractice C3_Ch04.indd 60 3/30/12 12:15 AM
Name: Date: ©
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
rivat
e Li
mite
d.
Extra Practice Course 3A 61
Solve. Show your work.
2. The growth of two plant saplings A and B, were observed for a period of 6 months. The graph shows the linear growth of the saplings, in centimeters.
a) Find the initial height of sapling A and sapling B.
b) Which sapling shows the greatest amount of growth during the 6 month time period? Explain.
3. The graph shows the cost, C, of renting a concert hall for t hours.
a) Find the vertical intercept of the graph and explain what information it gives about the situation.
b) Find the slope of the graph and explain what information it gives about the situation.
x
10
20
30
40
50
60
2 31 4 5 60
y
t
100
200
300
400
500
600
2 31 4 5 6 7 8 90
C
Sapling A
Sapling B
Growth of Plant Saplings
Number of Months
Time (h)
Hei
ght
(cm
)
Co
st ($
)
Concert Hall Rental Fee
MIF_ExtraPractice C3_Ch04.indd 61 3/30/12 12:15 AM
Name: Date:
© M
arsh
all C
aven
dish
Inte
rnat
iona
l (Si
ngap
ore)
Priv
ate
Lim
ited.
62 Chapter 4 Lesson 4.5
Solve. Show your work.
4. Two containers P and Q are filled with different amounts of water. Each container has a small hole. The graph shows the amount of water, V milliliters, left in each container after x minutes.
x
200
400
600
800
1000
20 40 60 800
V
a) Find the initial amount of water in each container.
b) Which container has a bigger hole?
Container Q
Container P
Am
oun
t o
f w
ater
(mL)
Amount of Water in Containers
Time (min)
MIF_ExtraPractice C3_Ch04.indd 62 3/30/12 12:15 AM
Name: Date: ©
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
rivat
e Li
mite
d.
Extra Practice Course 3A 63
Solve. Show your work.
5. A candle is 9 inches long. Nelson lights the candle and records the length of the candle, y inches, for x hours.
Number of Hours Candle Burns (x hours) 0 1 2 3 4
Height of Candle (y inches) 9 7 5 3 1
a) Graph the relationship between candle height and time. Use 2 grid squares to represent 1 unit on the horizontal axis for the x-interval 0 to 4 and 1 grid square for 1 unit on the vertical axis for the y-interval 0 to 9.
MIF_ExtraPractice C3_Ch04.indd 63 3/30/12 12:15 AM
Name: Date:
© M
arsh
all C
aven
dish
Inte
rnat
iona
l (Si
ngap
ore)
Priv
ate
Lim
ited.
64 Chapter 4 Lesson 4.5
b) Find the vertical intercept of the graph and explain what information it gives about the situation.
c) Find the slope of the graph and explain what information it gives about the situation.
d) Write an equation relating the height of the candle and the number of hours it is lit.
MIF_ExtraPractice C3_Ch04.indd 64 3/30/12 12:15 AM
© M
arsh
all C
aven
dish
Inte
rnat
iona
l (Si
ngap
ore)
Priv
ate
Lim
ited.
166 Answers
6. x 23 0 3
y 28 24 0
�2
�3
�5
�1
1
�4
�6
�7
�8
�1�2 1 2 3 4�3
y
0
y � x � 443
x(3, 0)
(0, �4)
(�3, 8)
7.
2
1
4
3
6
5
7
2 31 4
y
x0
(2, 5)
(3, 7)
8.
2
4
5
3
1
6
�4�5 �2�3 �1 21
y
x0
(�5, 6)
(0, 2)
9.
�2
�4
�3
�1
�6
�5
21 43 5 6
y
x0
(2, 3)
(3, 2)
10.
�4
�3
�2
1
�1�1 1 2�2�3�4
y
x0
(0, �1)
(�2, �4)
Lesson 4.5 1. a) From the graph, the vertical intercept
is 5. It represents the initial fixed amount for renting a bike.
b) The graph passes through (0, 5) and (6, 20).
Slope 5 � ��
�
20 56 0
156
52
The line has slope m 5 52
. It represents
the hourly rate for renting a bike.
It costs Max $20 to rent a bike for 6 hours.
2. a) From the graph, the initial height of sapling A is 40 centimeters and that of sapling B is 20 centimeters.
b) Sapling B. The graph of sapling B passes through (0, 20) and (4, 40).
Slope 5 � ��
�540 20
4 0204
So, the growth for sapling B is 5 centimeters.
The graph of sapling A passes through (0, 40) and (3, 50).
Slope 5 � ��
�350 40
3 0103
13
So, the growth of sapling A is
3 13
centimeters.
MIF_ExtraPractice_C3_Ch01-06_Ans.indd 166 30/03/12 9:00 AM
© M
arsh
all C
aven
dish
Inte
rnat
iona
l (Si
ngap
ore)
Priv
ate
Lim
ited.
Extra Practice Course 3A 167
3. a) From the graph, the vertical intercept is 100. It represents the initial rental charges of the concert hall.
b) The graph passes through (0, 100) and (6, 400).
Slope 5 � ��
�50400 100
6 03006
The slope represents the hourly rental charges of the concert hall. It is $50.
4. a) From the graph, the initial amount of water in container P is 1,000 milliliters and that in container Q is 800 milliliters.
b) The graph of P passes through (0, 1,000) and (40, 400).
Slope of P 5 � � ��
� �151,000 400
0 40600
40
The graph of Q passes through (0, 800) and (40, 400).
Slope of Q 5 � � ��
� �10800 400
0 40400
40
15 milliliters of water is leaking from container P per minute while 10 milliliters of water is leaking from container Q per minute. So, container P has a bigger hole.
5. a)
2
4
3
1
6
5
8
7
9
1 2 3 4
y
x0
Time (h)
Hei
ght
of
Can
dle
(in
.)
Height of Candle
b) From the graph, the vertical intercept is 9. It represents the initial height of the candle.
c) Slope 5 � ��
�29 7
0 1
The slope represents the rate at which the candle burns.
d) y 5 mx 1 b 9 5 0(22) 1 b b 5 9
An equation of the line is y 5 22x 1 9.
Brain@Work 1. a) Let the speed of the bus as it passes the
stop be a meters per second.
The area under the speed-time graph is the distance traveled by the bus. So, the area is 50 square units.
Area of trapezium 5 50
12
(5 2 0)(a 1 8) 5 50
�a5( 8)2
5 50
�a5( 8)2
? 2 5 50 ? 2
5(a 1 8) 5 100
��a5( 8)5
1005
a 1 8 5 20
a 1 8 2 8 5 20 2 8
a 5 12
So, the speed of the bus as it passes the stop is 12 meters per second.
b) Rate of slowing down 5 slope of the graph
�
� �
�
�
12 80 5
45
5 20.8
The rate of deceleration is 0.8 meter per square second.
c) An equation of the line is y 5 20.8t 1 12.
2. a) The speed of the car is increasing.
b) The car is slowing down.
c) The car is not moving.
d) The speed of the car is increasing.
e) The car is slowing down.
f) The car is not moving.
Cumulative Practice for Chapters 3 to 4 1. 3(2x 2 4) 2 7 5 23 6x 2 12 2 7 5 23 6x 2 19 5 23 6x 2 19 1 19 5 23 1 19 6x 5 42
�
x6
6
42
6
x 5 7
MIF_ExtraPractice_C3_Ch01-06_Ans.indd 167 30/03/12 9:00 AM
