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Turn It In Systems of Linear Equations Name: Answer the following: We now consider how two or more linear functions interact with each other. As consumers, we are often faced with choices. In this lesson, we will solve systems of equations in order to determine the best deal for our needs. Much of mathematics work we have done this semester has depended on making connections among representations. To study and solve systems of equations, the interrelationships between tables, graphs, and equations are critical. Think about the contexts, and create tables, graphs and equations to extend what you have learned about linear functions to work with them two or more at a time. Fitness Plans By now, you are proficient at finding equations. You will use tables to locate an interval over which two or more of the fitness plans cost the same amount. You will refine your search for an intersection point with graphs and then by solving pairs of equations. 1. Consider payment plans for three different fitness centers:  Shape Up charges an initiation fee of $39 plus $35 per month per person.  Fitness Fun charges an initiation fee of $75 plus $20 per month per person.  Be Your Best has no initiation fee and charges $52 per month per person. Complete the table showing the total cost for the first 6 months for each fitness company's payment plan (initiation fees are only charged once.) Amount Paid so far (in dollars) Month Shape Up Fitness Fun Be Your Best 1 74 95 52 2 109 115 104 3 144 135 156 4 179 155 208 5 214 175 260 6 249 195 312 x

2. For each set of data, make a graph (month, amount paid so far). Label each graph with the company's name. Shape Up

Fitness Fun

Be Your Best

3. a. Which company charges the most after 6 months of membership? How do you know? 312 the largest of three values 249, 175, 312. Be Your Best charges most. b. How can you tell from a graph? For the third graph the value ordinate for the abscise x=6 is the largest c. How can you tell from a table? In the raw correspondent to 6 months the last value is the largest d. Which company has the steepest graph? Be Your Best Why does that make sense? The steepest graph is for the function which grows most quickly. Since it grows quickly, for the same values of x the values of y are larger starting from some value. 4. What does the y-intercept represent for each fitness payment plan? It represents an initial fee 5. Find an equation that fits each data set. Write your equation in the form y = mx + b. Include the equation in the last row of the table. Shape Up Fitness Fun Be Your Best 6. You have $500 to spend on a fitness plan this year. Show your work. a. Which fitness plans can you afford and why? Shape Up

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