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Essential Question: What are some facts that you can find out about a real-world situation from reading a graph that models a situation.

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You can model many real world situations with linear equations. Remember that a graph of an equation shows the solutions of that equation However, for discrete situations, not every point may represent a reasonable value. ◦ Remember: Discrete Data is Counted ◦ Continuous Data is Measured

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Example 1 ◦ A car dealership has 40 cars in stock. The auto manufacturer will deliver new cars to the dealership by car carrier. Each carrier holds 6 cars. Write a linear function that relates the number of carriers used to the total number of cars at the dealership. Graph the function that models the situation. The total equals 40 plus 6 times the number of number of cars car carriers Let x = the number of car carriers Let y = the total number of cars y = x

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Example 1 (continued) ◦ y = x ◦ Let’s reorder the right side…y = 6x + 40 ◦ Start with the y-intercept b = 40 ◦ Use rise / run to make successive points Up 6, over 1 ◦ Discrete points (not a line) We’re counting # of car carriers

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YYour Turn ◦A◦A sporting goods store sells cans of tennis balls. There are 3 tennis balls in each can. Write a linear function that relates the number of cans to the total number of tennis balls. tt = number of tennis balls c = number of cans tt = 3n

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Example 2: Analyzing Linear Graphs ◦ Students in a ninth-grade class drew the following graph to represent how much money would be in the class fund after washing cars at a fundraiser. ◦ What does the slope and y-intercept of graph mean for the given situation? y-intercept is $25 Slope is 3 It means the class charged $3/car, and started with $25 in their account.

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If the graph had the same slope, but a y-intercept of 15, what would that mean? ◦ It would mean that the class started with $15 instead of $25 If the graph had a slope of 5, what could you conclude? ◦ That the class charged $5/car instead of $3.

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YYour Turn ◦S◦Suppose you drew the following graph to represent how far you ride your bike at a steady rate. ◦W◦What is your rate? 112 miles/hr ◦I◦If the graph had a slope of 10, what could you conclude about your bike ride? YYour rate would be 10 miles/hr

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Assignment ◦ Worksheet #6-3 ◦ All problems

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