Price
(dollars per
ride)
Balloon rides
(number per day)
10°C 20° C 30° C
5 32 40 50
10 27 32 40
15 18 27 32
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14 AP P ENDIX
Answers to Appendix Additional Problems and Applications
Use the spreadsheet to work Problems
12 to 14. The spreadsheet provides
data on oil and gasoline: Column A is
the year, column B is the price of oil
(dollars per barrel), column C is the
price of gasoline (cents per litre),
column D is oil production, and column
E is the quantity of gasoline refined
(both in millions of barrels per day).
12. Draw a scatter diagram of the
price of oil and the quantity of oil produced. Describe the relationship.
The scatter diagram between the price of a barrel of oil and the quantity of oil produced
shows a weak negative relationship.
13. Draw a scatter diagram of the price of gasoline and the quantity of gasoline
refined. Describe the relationship.
The scatter diagram between the price of a gallon of gasoline and the quantity of gasoline
refined shows a weak negative relationship.
14. Draw a scatter diagram of the quantity of oil produced and the quantity of
gasoline refined. Describe the relationship.
The scatter diagram between the quantity of oil produced and the quantity of gasoline refined
shows a positive relationship.
Use the following data to work
Problems 15 to 17.
Draw a
graph
that
shows the relationship between the
two variables x and y in the table
below.
To make a graph that shows the
relationship between x and y, plot the x-
variable on the x-axis and the y-variable
on the y-axis. The graph is shown in
Figure A1.3.
15. a. Is the relationship positive or
negative?
The relationship is negative because x
and y move in opposite directions: As x
increases, y decreases.
A B C D E
1 2006 66 262 5.1 15.6
2 2007 72 284 5.1 15.4
3 2008 100 330 5.0 15.3
4 2009 62 241 5.4 14.8
5 2010 79 284 5.5 15.2
6 2011 95 358 5.6 15.1
7 2012 94 368 6.5 15.5
8 2013 98 358 7.5 15.2
9 2014 93 344 8.8 15.5
10 2015 49 252 9.4 16.6
11 2016 45 225 9.0 16.4
x 0 1 2 3 4 5
y 25 24 22 18 12 0
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WH AT IS ECO NO MICS? 1 5
b. Does the slope of the relationship become steeper or flatter as the value of x
increases?
The slope becomes steeper as x increases.
c. Think of some economic relationships that might be similar to this one.
The less expensive a good, the greater is the number of people who buy it. The higher the
interest rate, the smaller is the number of people who take out home mortgages. The less
expensive gasoline, the greater the miles car owners drive.
16. Calculate the slope of the relationship between x and y when x equals 3.
The slope equals −5. The slope of the curve at the point where x is 3 is equal to the slope of
the tangent to the curve at that point. Draw the tangent line at the point in Figure A1.3 where x
is 3 and y is 18. Now calculate the slope of this tangent line by finding another point on the
tangent. When x equals 5, y equals 10 on the tangent, so another point is x equals 5 and y
equals 10. The slope equals the change in y, −8, divided by the change in x, 2, so the slope is
−4.
17. Calculate the slope of the relationship across the arc as x increases from 4 to 5.
The slope is –12. The slope of the relationship across the arc when x increases from 4 to 5 is
equal to the slope of the straight line joining the points on the curve at x equals 4 and x equals
5. When x increases from 4 to 5, y falls from 12 to 0. The slope equals the change in y, −12
(0 minus 12), divided by the change in x, 1 (5 minus 4), so the slope across the arc is −12.
18. Calculate the slope of the curve in Figure A1.4 at point A.
The slope is −2. The curve is a straight
line, so its slope is the same at all points
on the curve. Slope equals the change in
the variable measured on the y-axis
divided by the change in the variable
measured on the x-axis. To calculate the
slope, select two points on the line. One