S ECTION 3-5: L INEAR F UNCTIONS AS M ATHEMATICAL M ODELS.

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Presentation transcript:

S ECTION 3-5: L INEAR F UNCTIONS AS M ATHEMATICAL M ODELS

O BJECTIVE Given a situation in which two real-world variables are related by a straight-line graph, be able to: Sketch the graph. Find the particular equation. Use the equation to predict values of either variable. Figure out what the slope and intercepts tell you about the real world.

E XAMPLE 1 As you drive home from the football game, the number of kilometers you are away from the game depends on the number of minutes you have been driving. Assume that distance varies linearly with time. Suppose that you are 11 km from home you have been driving for 10 minutes and 8 km from home when you have been driving for 15 minutes. Define variables for distance and time, and sketch the graph. Find the particular equation expressing distance in terms of time. Predict your distance away from home when you have been driving for: 20 minutes 25 minutes 30 minutes What are the intercepts and what do they represent in the real world. In what domain do you have reasonable answers? What are the units of the slope?

E XAMPLE 2 A local donut establishment charges 20 cents for each donut, plus a one-time charge of 15 cents for the box, the service, etc. Write an equation expressing the amount charged as a function of the number of donuts bought. Explain why the function is linear. Predict the price of a box with a dozen donuts. How many donuts would be in a box priced at $3.55? Plot a graph of the function, using a reasonable domain.

E XAMPLE 3 Assume that the maximum speed your car will go is a linear function of the steepness of the hill it is going up or down. Suppose the car will go a maximum of 55 mph up a 5 O hill and 104 mph down a 2 O. Write the particular equation expressing the maximum speed in terms of steepness. How fast would you go down a 7 O hill? If your top speed is 83 mph, how steep is the hill? Is it up or down? What are the intercepts and what do they represent? Sketch a graph, using a reasonable domain.

HOMEWORK: p. 98 #1, 3 and 15