1 MAC1105, College Algebra Study Questions for Common Final ...

d. Line is horizontal and passes through (1.0, 72.).
e. Line is vertical and passes through (275, 1029).
f. Line is perpendicular to y = -2x + 7 and passes through (5,2).
19. The Gas Guzzler Tax is imposed on manufacturers on the sale of new-model cars (not minivans,
sport utility vehicles, or pickup trucks) whose fuel economy fails to meet certain statutory
regulations, to discourage the production of fuel-inefficient vehicles. The tax is collected by the
IRS and paid by the manufacturer. The table shows the amount of tax that the manufacturer
must pay for a vehicle’s miles per gallon fuel efficiency.
Gas Guzzler Tax
MPG Tax Per Car
12.5 $6400
13.5 $5400
14.5 $4500
15.5 $3700
16.5 $3700
17.5 $2600
18.5 $2100
19.5 $1700
20.5 $1300
21.5 $1000
22.5 $0
(Source: http://www.epa.gov/otaq/cert/factshts/fefact o.1. pdf)
a. Plot the data, verify that they are roughly linear, and add a line of best fit.
b. Choose two points on the line, find the slope, and then form a linear equation with x as the
fuel efficiency in mpg and y as the tax in dollars.
c. What is the rate of change of the amount of tax imposed on fuel-inefficient vehicles?
Interpret the units.
20. Create the system of equations that produced the accompanying graph. Estimate the solution
for the system from the graph and then confirm using your equations.
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