Keeping Safe
0 The managers of a shopping center want to
upgrade their security system.
0 Two providers bid for the job.
0 Super Locks will charge $3,975 to install
the equipment and the $6.00 per day to
monitor the system and respond to the
alerts.
0 Fail Safe will charge $995 to install the
equipment and then $17.95 per day to
monitor the system and respond to alerts.
0 Both companies are reliable and capable,
so the choice comes down to cost.
The cost of the security services from Super
Locks and Fail Safe depends on the number
of days the company provides service.
0 Write an equation that can be used
to calculate the cost for “x”
number of days for each company.
0 Use the format: y = mx + b
Instead of using “y”, use “C” for
cost.
0 The one time charge is b, the yintercept. That’s how much you
would pay with zero days of
monitoring.
0 The repeating charge is the
slope. That’s the daily monitoring
fee.
Write the Equations
0 Super Locks:
0 C = 6x + 3978
0 Fail Safe:
0 C = 17.95x + 995
Which company is the better deal?
What does the best deal depend on?
TIME
Graph the two equations to find out
when each company is the best price.
0 To graph each
equation,
substitute a
number of days
in for x and solve
for C.
0 This will make a
table of values.
Plot each
ordered pair.
Super Locks
Fail Safe
Days
(x)
Cost
(C)
Days
(x)
Cost
(C)
0
3978
0
995
100
4578
100
2790
200
5178
200
4585
300
5778
300
6380
400
6378
400
8175
500
6978
500
9970
Fail Safe
Super Locks
Which company is the better deal?
Or, when is EACH company the better deal?
How can you tell?
Use the graph to answer the
following questions…
1. For what number of days will
Fail Safe
Super Locks
the costs for the two
companies be the same?
What is the cost?
2. For what number of days will
Super Locks cost less than
Fail Safe?
3. For what number of days will
Super Locks cost less than
$6,000?
4. What is the cost of one year
of service from Fail Safe?
Make a graph by plotting each plant’s
ordered pairs (W, H).
Practice:
14
0 Plant A and Plant B are on different
watering schedules. This affects
their rate of growth. Compare the
growth of the two plants to
determine when their heights will
be the same.
0 Let W = number of weeks
0 Let H = height of the plant after W
weeks
Plant A
Plant B
H
E
I
G
H
T
12
10
8
6
4
2
0
1
2
3
4
5
Weeks
Weeks
(W)
Height
(H)
Weeks
(W)
Height
(H)
0
4
0
2
1
6
1
6
2
8
2
10
3
10
3
14
At which week do the plants have the
same height? What is their height?