72.Demand for an item is often closely related to its price. As price increases, demand de-
creases, and as price decreases, demand increases. Suppose demand for a video game is
2000 units when the price is $40 and is 2500 units when the price is $30.
(a)Let xbe the price and ybe the demand for the game. Graph the two given pairs of
prices and demands.
(b)Assume that the relationship is linear. Draw a line through the two points from
part (a). From your graph, estimate the demand if the price drops to $20.
(c)Use the graph to estimate the price if the demand is 3500 units.
73.In the United States, sporting goods sales y(in billions of dollars) from 2000 through
2006 are shown in the graph and modeled by the linear equation
where x= 0 corresponds to 2000, x= 1 corresponds to 2001, and so on.
y=3.018x+72.52,
198 CHAPTER 3 Linear Equations and Inequalities in Two Variables; Functions
0
70
75
80
85
90
95
123456
Year
Source: National Sporting Goods Association.
Sales (in billions of dollars)
y
x
Sporting Goods Sales
(a)Use the equation to approximate sporting goods sales in 2000, 2004, and 2006.
Round your answers to the nearest billion dollars.
(b)Use the graph to estimate sales for the same years.
(c)How do the approximations using the equation compare with the estimates from the
graph?
74.U.S. per capita consumption of cheese in-
creased for the years 1980 through 2005 as
shown in the graph. If represents 1980,
represents 1985, and so on, per capita
consumption yin pounds can be modeled by
the linear equation
(a)Use the equation to approximate cheese
consumption (to the nearest tenth) in 1990,
2000, and 2005.
(b)Use the graph to estimate consumption for
the same years.
(c) How do the approximations using the
equation compare with the estimates from
the graph?
y=0.5383x+18.74.
x= 5
x= 0
Source: U.S. Department of Agriculture.
Year
5 10 15 20 25
0
15
20
25
30
35
y
Consumption (in pounds)
x
Cheese Consumption
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