2.4 Models of Linear Equations
1. Phone Charges – The monthly cost C, in dollars, of a certain cell phone plan is given by the function
𝐶(𝑥) = 0.38𝑥 + 5, where x is the number of minutes used on the phone.
a) Graph the equation on your calculator. Be sure to find an appropriate window.
b) Find the cost of the plan if you talk on the phone for 50 minutes __________________
c) Suppose that your monthly bill is $29.32. How many minutes did you use the phone? (show work)
2. Health Expenditures – The total private health expenditures H, in billions of dollars, is given by the function
𝐻(𝑥) = 26𝑡 + 411,where t is the number of years since 1990.
a) Graph the equation in your calculator. Be sure to find an appropriate window.
b) What was the total private health expenditures in 2000? ___________________
c) In what year will total private health
expenditures be $879 billion? (show work)
d) In what year will total private health
expenditures exceed $1 trillion (1000 billion)?
(show work)
3. Supply and Demand – Suppose that the quantity supplied S and quantity demanded D of hot dogs at a basketball game
are given by the following functions:
𝑆(𝑝) = −2000 + 3000𝑝
𝐷(𝑝) = 10,000 − 1000𝑝
where p is the price in dollars. The equilibrium price of a market is defined as the price at which quantity supplied equals
quantity demanded (S = D).
a) Graph the two equations on the same graph. Be sure to find an appropriate window.
b) Find the equilibrium price for hot dogs at the basketball game. ____________________
What is the equilibrium quantity? ___________________
c) Determine the prices for which quantity demanded is less than quantity supplied. (show work)
4. Mortgage Qualification – The amount of money that a lending institution will allow you to borrow mainly depends on
the interest rate and your annual income. The following data represent the annual income, I, required by a bank in order to
lend L dollars at an interest rate of 7.5% for 30 years.
Annual Income
15,000
20,000
25,000
30,000
35,000
40,000
Loan Amount
44,600
59,500
74,500
89,400
104,300
119,200
Annual Income
45,000
50,000
55,000
60,000
65,000
70,000
Loan Amount
134,100
149,000
163,900
178,800
193,700
208,600
Let I represent the independent variable (x) and L the dependent variable (y).
a) Use your graphing calculator to create a scatter plot of the data
b) Find the equation for the line of best fit _________________________
c) Graph the line of best fit on the calculator
d) What loan amount would an individual qualify for if her income is $42,000 a year? ___________________
5. Advertising and Sales Revenue – A marketing firm wishes to find a function that relates the sales S of a product and
A, the amount spent on advertising the product. The data are obtained from past experience. Advertising and sales are
measured in thousands of dollars.
a) Does the relation defined by the set of ordered pairs (A, S) represent a function? Why or why not?
b) Create a scatter plot of the data
c) Find and graph the equation for the line of best fit
d) Express the relationship found in part (c) using function notation ______________________________
e) What is the domain of the function? _____________________
f) Predict sales if advertising expenditures are $25,000. __________________________
g) If sales are $400,000 predict how much the company might have spent on advertising. (show work)