The pattern made by the dots tells us that when the interest rate increases, the
unemployment rate usually decreases so there is a negative relationship.
A B C D E
1 2006 2.5 4.9 2.7 4.6
2 2007 4.1 4.5 1.8 4.6
3 2008 0.1 1.4 -0.3 5.8
4 2009 2.7 0.2 -2.8 9.3
5 2010 1.5 0.1 2.5 9.6
6 2011 3.0 0.1 1.6 8.9
7 2012 1.7 0.1 2.2 8.1
8 2013 1.5 0.1 1.7 7.4
9 2014 0.8 0.0 2.4 6.2
10 2015 0.7 0.1 2.6 5.3
11 2016 2.1 0.3 1.6 4.9
Copyright © 2019 Pearson Canada Inc.
12 AP P ENDIX
Use the following news clip to work Problems 4 to 6.
Kong Tops the Box Office
Source: boxofficemojo.com
Data for weekend of February 10-12, 2017
4. Draw a graph of the relationship between the revenue per theatre on the y-axis
and the number of theatres on the x-axis. Describe the relationship.
The graph shows a positive relationship.
5. Calculate the slope of the relationship between 3,846 and 4,071 theatres.
The slope equals the change in revenue per theatre divided by the change in the number of
theatres. The slope equals ($9,362 − $15,867)/(4,071 − 3,846), which equals -$28.91 per
theatre.
6. Calculate the slope of the relationship between 4,071 and 3,143 theatres.
The slope equals the change in revenue per theatre divided by the change in the number of
theatres. The slope equals ($6,600 − $9,362)/(3,143 − 4,071), which equals $2.98 per theatre.
7. Calculate the slope of the relationship shown in Figure A1.1.
The slope is −5/4. 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 point is at 10
on the y-axis and 0 on the x-axis, and
another is at 8 on the x-axis and 0 on
the y-axis. The change in y from 10 to
0 is associated with the change in x
from 0 to 8. The slope of the curve
equals −10/8, which equals −5/4.
Movie
Theatres
(number)
Revenue
(dollars per
theatre)
Kong: Skull Island 3,846 $15,867
Logan 4,071 $9,362
Get Out 3,143 $6,600
The Shack 2,888 $3,465
Copyright © 2019 Pearson Canada Inc.
WH AT IS ECO NO MICS? 1 3
Use the relationship shown in Figure
A1.2 to work Problems 8 and 9.
8. Calculate the slope of the relationship at
point A and at point B.
The slope at point A is −2, and the slope at
point B is −0.25. To calculate the slope at a
point on a curved line, draw the tangent to the
curved line at the point. Then find a second
point on the tangent and calculate the slope
of the tangent.
The tangent at point A cuts the y-axis at 10.
The slope of the tangent equals the change in
y divided by the change in x. The change in y
equals −4 (6 minus 10) and the change in x
equals 2 (2 minus 0). The slope at point A is
−4/2, which equals −2.
The tangent at point B goes through the point
(4,2). The change in y equals −0.5, and the
change in x equals 2. The slope at point B is
−0.25.
9. Calculate the slope across the arc AB.
The slope across the arc AB is −1.125. The slope across the arc AB equals the change in y,
which is 4.5 (6.0 minus 1.5) divided by the change in x, which equals −4 (2 minus 6). The
slope across the arc AB equals 4.5/−4, which is −1.125.
Use the table to work Problems 10 and 11. The table gives the price of a balloon
ride, the temperature, and the number of rides a day.
10. Draw a graph to show the
relationship between the price
and the number of rides, when
temperature is 20°C. Describe this
relationship.
The graph plots the price on the y-
axis and the number of rides on the
x-axis using the number of balloon rides in the column of the table labelled 20°C. The
relationship between the price and the number of rides is negative. As the price rises, the
number of rides decreases.
11. What happens in the graph in Problem 10 if the temperature rises to 30°C?
If the temperature rises to 30°C, the curve shifts rightward. At every price, more balloon rides
are taken when the temperature is 30°C rather than 20°C.