point is at 18 on the y-axis and 0 on the x-
axis, and another is at 9 on the x-axis and
0 on the y-axis. The change in y from 18
to 0 is associated with the change in x
from 0 to 9. Therefore the slope of the
curve is −18/9, which equals −2.
Copyright © 2019 Pearson Canada Inc.
16 AP P ENDIX
Use Figure A1.5 to work Problems 19 and 20.
19. Calculate the slope at point A and at
point B.
The slope at point A is −4, and the slope
at point B is −1. To calculate the slope at
a point on a curved line, draw the tangent
to the 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 x-axis at
2.5. The slope of the tangent equals the
change in y divided by the change in x.
The change in y equals 6 (6 minus 0) and
the change in x equals −1.5 (1 minus 2.5).
The slope at point A is 6/−1.5, which
equals −4. Similarly, the slope at point B
is −1. The tangent at point B cuts the y-
axis at 5. The change in y equals 3, and
the change in x equals −3.
20. Calculate the slope across the arc AB.
The slope across the arc AB is −2. The
slope across the arc AB equals the change in y, which is 4 (6 minus 2) divided by the change
in x, which equals −2 (1 minus 3). The slope across the arc AB is 4/−2, which equals −2.
Use the following table to work Problems 21 to 23.
The table gives information about umbrellas: price, the number purchased, and rainfall in
millimeters (mms).
21. Draw a graph to show
the relationship between the
price and the number of
umbrellas purchased,
holding the amount of
rainfall constant at 200 mm.
Describe this relationship.
To draw a graph of the relationship between the price and the number of umbrellas when the
rainfall equals 200 mm, keep the rainfall at 200 mm and plot the data in that column against
the price. The relationship between the price and the number of umbrellas is a negative
relationship.
22. What happens in the graph in Problem 21 if the price rises and rainfall is
constant?
If the price rises, the number of umbrellas decreases. There is a movement upward along the
(unchanged) curve.
23. What happens in the graph in Problem 21 if the rainfall increases from 200 mm to
400 mm?
The curve when the rainfall is 400 mm lies to the right of the curve when the rainfall is 200
mm showing that at every price, more umbrellas are purchased when the rainfall is 400 mm
than when the rainfall is 200 mm.
Price
(dollars per
umbrella)
Umbrellas
(number purchased per day)
0 mm 200 mm 400 mm
20 4 7 8
30 2 4 7
40 1 2 4