The rows in some movie theaters are so steep that there are no bad seats. We saythat the theater has a steep slope. Slope is the ratio of the rise, or the vertical change, to the run, or the horizontal change.
The slope of
the floor in the theater at the right is 
.
On the graph below, the line passes through points at (4, 0) and (11, 3).
The change in y or rise is 3 – 0 or 3, while the change in x or
run is 11 – 4 or 7. Therefore, the slope of this line is 
.
Example
Determine
the slope of each line.
1.
Alternative Solutions:
2.
Alternative Solutions:
In Example
1, suppose 2 – 6 had been used as the change in y and 0 – 7 had been
used as the change in x. Since 
is also equal to 
, it does not matter which order is chosen. However, the
coordinates of both points must be used in the same order.
In many
real-world applications, the slope is the rate of change.
Example
Income Link
3. The
graph at the right shows the hours worked and income for Helena and Steve. Find
the slope of each line. To what does the slope refer?
Alternative Solutions:
The graph represents
Helena‘s income and Steve’s income. The steepness depends on their hourly pay
rate. So, the slope refers to each person’s pay rate. Helena makes $10 per hour
and Steve makes $6 per hour. Notice that the domain and range are nonnegative
numbers since they cannot work fewer than 0 hours or earn less than $0.
Look at the
pattern in the graph at the right. Each time x increases 3 units, y decreases 1
unit.
Example
4. A
line contains the points whose coordinates are listed in the table. Determine
the slope of the line.
Alternative Solutions:
Each time x
decreases 2 units, y increases 3 units.
The slope of the line containing
these points is 
.
The examples
above suggest the following.
Example
Determine
the slope of each line.
5.
the
line through (2, 9) and (6, 9)
Alternative Solutions:
6.
the
line through (3, –2) and (–4, 7)
Alternative Solutions:
The slopes of lines can be summarized
as follows.
Sumber
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