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**6-3: Applying Linear Functions**

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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**6-3: Applying Linear Functions**

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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**6-3: Applying Linear Functions**

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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**6-3: Applying Linear Functions**

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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**6-3: Applying Linear Functions**

Your Turn 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. t = number of tennis balls c = number of cans t = 3n

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**6-3: Applying Linear Functions**

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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**6-3: Applying Linear Functions**

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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**6-3: Applying Linear Functions**

Your Turn Suppose you drew the following graph to represent how far you ride your bike at a steady rate. What is your rate? 12 miles/hr If the graph had a slope of 10, what could you conclude about your bike ride? Your rate would be 10 miles/hr

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**6-3: Applying Linear Functions**

Assignment Worksheet #6-3 All problems

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