Page 122 - Math Course 3 (Book 1)

Linear Equations: Rate of Change

Airlines MO. 4 - L1b
The graph shows the number of airplane departures
in the United States in recent years. Find the rates of
change for 1990-1995 and 1995-2000. Finding the Slope of a Line

A.1,200,000 per year; U.S Airline Departures
900,000 per year 9.5

B. 8,100,000 per year; 9.0 Key Concept
8.5
9,000,000 per year Departures (millions) 8.0
7.5
C.5 per year; 5 per year 7.0 Slope
6.5
D. 240,000 per year; 0 Words The slope of a line is the ratio of the rise
180,000 per year ‘90 ‘95 ‘00 to the run.
year

Symbols The slope m of a nonvertical line through
Answer
any two points, (x , y ) and (x , y ), can be
2
2
1
1
found as follows.
Explain the meaning of the slope in each case.
y – y 1 change in y
2
A. For 1990-1995, the number of airplane m = x – x 1 change in x
2
departures increased by about 240,000 flights Graph
each year. For 1995-2000, the number of airplane y
departures increased by about 180,000 flights x – x 1
2
each year.
y – y
2 1 (x , y )
B. The rate of change increased by the same 2 2
amount for 1990-1995 and 1995-2000. (x – y ) x
1
1
0
C. The number airplane departures decreased by
about 240,000 for 1990-1995 and 180,000 for
1995-2000.
Slope
D. For 1990-1995 and 1995-2000 the number of
airplane departures was the same. positive slope negative slope
y y
Answer

How are the different rates of change shown on 0 x 0 x
the graph? line slopes up from line slopes down
left to right from left to right
A. There is a greater vertical change for 1990-1995
than for 1995-2000. Therefore, the section of
the graph for 1990-1995 has a steeper slope. slope of zero undefined slope

B. They have different y-values. y y

C. The vertical change for 1990-1995 is negative,
and for 1995-2000 it is positive.
0 x 0 x
D. There is no difference shown in the graph. horizontal line vertical line

Answer

114