Two quantities that are changing with time can be compared by drawing both
lines on the same graph.600 Chapter 7 Graphs and Statistics
StrategyWe will determine whether the graph is rising, falling, or is horizontal.
WHYWhen the graph rises as we read from left to right, the number of ATMs is
increasing. When the graph falls as we read from left to right, the number of ATMs
is decreasing. If the graph is horizontal, there is no change in the number of ATMs.
Solution
a.To find the number of ATMs in 2001, we follow the dashed blue line from the
label 2001 on the horizontal axis straight up to the line graph. Then we extend
directly over to the scale on the vertical axis, where the arrowhead points to
approximately 325. Since the vertical scale is in thousands of ATMs, there were
about 325,000 ATMs in 2001 in the United States.
b.This line graph is composed of seven line segments that connect pairs of
consecutive years. The steepest of those seven segments represents the
greatest increase in the number of ATMs. Since that segment is between
the 2000 and 2001, the greatest increase in the number of ATMs occurred
between 2000 and 2001.
c.The only line segment of the graph that falls as we read from left to right is the
segment connecting the data points for the years 2006 and 2007. Thus, the
number of ATMs decreased from 2006 to 2007.
d.The line segment connecting the data points for the years 2005 and 2006 appears
to be horizontal. Since there is little or no change in the number of ATMS for
those years, the number of ATMs remained about the same from 2005 to 2006.EXAMPLE (^7) Trains The line graph below shows the movements of two
trains. The horizontal axis represents time, and the vertical axis represents the
distance that the trains have traveled.
a.How are the trains moving at time A?
b.At what time (A, B, C, D, or E) are both
trains stopped?
c. At what times have both trains traveled
the same distance?
StrategyWe will determine whether the
graphs are rising or are horizontal. We will
also consider the relative positions of the
graphs for a given time.
WHYA rising graph indicates the train is moving and a horizontal graph means it
is stopped. For any given time, the higher graph indicates that the train it represents
has traveled the greater distance.
Solution
The movement of train 1 is represented by the red line, and that of train 2 is
represented by the blue line.
a.At time A, the blue line is rising. This shows that the distance traveled by train
2 is increasing. Thus, at time A, train 2 is moving. At time A, the red line is
horizontal. This indicates that the distance traveled by train 1 is not changing:
At time A, train 1 is stopped.
b.To find the time at which both trains are stopped, we find the time at which both
the red and the blue lines are horizontal. At time B, both trains are stopped.
A
Time
Train 1
Train 2
Distance traveled
B C D E
Self Check 7
TRAINSIn the graph for
Exercise 7, what is train 1 doing
at time D?
Now TryProblems 53, 55, and 59