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##### Graphs of Linear Systems

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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?