5.3 and 5.4
Rate of Change and Slope
Rate of Change is a ratio
It compares:
Change in dependent variable
Change in independent variable
Slope is the ratio of the change in y
to the change in x.
change in the rise
y
x = change in the run
Calculate the slope of the line containing the
points (-2, 4) and (-5, -8) two different ways.
.
Example:
In 1985, the cost of a postage stamp was 22 cents.
In 1988, the cost of a postage stamp was 25 cents.
Name the dependent variable:
Name the independent variable:
Find the rate of change:
20
10
Year
1991
1990
1989
1988
1987
1986
8
6
4
2
1985
Cost (cents)
30
Example:
In 1988, the cost of a postage stamp was 25 cents.
In 1990, the cost of a postage stamp was 25 cents.
Find the rate of change:
20
10
Year
1991
1990
1989
1988
1987
1986
8
6
4
2
1985
Cost (cents)
30
Find the rate of change from a graph:
Sketch a line that has . . .
a positive slope
a zero slope
a negative slope
an undefined slope
Calculate the slope of the line containing the points:
(6, 1) and (-4, -3)
This table of values shows a linear relationship.
Calculate the slope.
x -3 0 3 6 9
y 4 4 4 4 4
Find the slope of the line.
Then tell what the slope represents.
Plant Growth
Height (cm)
40
30
20
10
10
20
30
40
50
60
70
Time (days)