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Graphs of Linear Systems What is the best deal?
Keeping Safe • The managers of a shopping center want to upgrade their security system. • Two providers bid for the job. • 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. • Fail Safe will charge $995 to install the equipment and then $17.95 per day to monitor the system and respond to alerts. • 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. • Write an equation that can be used to calculate the cost for “x” number of days for each company. • Use the format: y = mx + bInstead of using “y”, use “C” for cost. • The one time charge is b, the y-intercept. That’s how much you would pay with zero days of monitoring. • The repeating charge is the slope. That’s the daily monitoring fee. Super Locks is $3,978 to install and $6.00 per day to monitor. Fail Safe is $995 to install and $17.95 per day to monitor.
Write the Equations • Super Locks: • C = 6x + 3978 • Fail Safe: • C = 17.95x + 995 Super Locks is $3,978 to install and $6.00 per day to monitor. Fail Safe is $995 to install and $17.95 per day to monitor. 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. • To graph each equation, substitute a number of days in for x and solve for C. • This will make a table of values. Plot each ordered pair. 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… • For what number of days will the costs for the two companies be the same? What is the cost? • For what number of days will Super Locks cost less than Fail Safe? • For what number of days will Super Locks cost less than $6,000? • What is the cost of one year of service from Fail Safe? Fail Safe Super Locks
Make a graph by plotting each plant’s ordered pairs (W, H). Practice: 14 12 10 8 6 4 2 H E I G H T • 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. • Let W = number of weeks • Let H = height of the plant after W weeks 0 1 2 3 4 5 Weeks At which week do the plants have the same height? What is their height?