Warm Up A school club pays $35.75 to rent a video cassette player to show a movie for a fund raising project. The club charges 25 cents per ticket for the movie. Complete the table to show the profit the club should expect to have in terms of the number of tickets they sell to the movie. 2.Write a function P(n) to express the profit in terms of the number of tickets sold. 3. Use your function to find the profit made if they sold 20tickets. 4. Use your function to find the number of tickets they must sell to break even (zero profit) 5. Explain what is being answered when you evaluate P(500).

Homework Questions…

More Linear Functions Rate of Change, Appropriate Domain, Line of Best Fit, etc.

The height h in centimeters of a stack of n cups is given by the linear function h(n) = 0.4n Determine the value of h(4). What is the meaning of this value in terms of the cups and height? Determine the value of h(1.5). Does this point have meaning in terms of the cups and height of the stack? Explain. If the maximum height of the box containing the cups is 33.5 cm, what is the maximum number of cups that will fit in the box? What is the appropriate domain for this situation?

The slope of a graph can be expressed as a rate of change. Linear functions have a CONSTANT rate of change. Speed is a familiar rate of change. To interpret a constant speed of 25 mph as a rate of change, one could say that a car traveling at this speed goes an additional 25 miles for each additional hour of travel.

The height h in centimeters of a stack of n cups is given by the linear function h(n) = 0.4n Interpret the slope of the line as a rate of change that compares a change in height to a change in the number of cups.

YOUR TURN Jeremy collected the following data on stacking chairs. How do you know this data is linear? Write a linear function that best models the data. Interpret the slope as a rate of change If the room has 8 ft ceilings, what is the appropriate domain for this situation?

Citydog Screen Printers makes special order T-shirts. Recently, Citydog received two orders for a special T-shirt design. The first order was for 40 T-shirts at a total cost of $295, and the second order was for an additional 80 T-shirts at a total cost of $565. Each order included a standard shipping and handling charge. Write a linear function to model the cost, C, of ordering n shirts. Interpret the slope as a rate of change. Explain the meaning of the y-intercept of your function in terms of shirts and cost.

not exactly linear… The age and weight of a group of female children are given in the table below. Age(months) Weight (lbs) Use your calculator to write the regression equation for the data. Let x = age and y = weight 1.What is the slope of your equation? Interpret the slope in terms of age and weight. 2.Use the equation to predict the weight of a girl 5 years old. 3.Use the equation to predict the age of a girl who weighs 31 pounds.