Slope
Slopes (or steepness) of lines are seen everywhere.
The steepness of the roof of a house is referred to as the pitch of the roof by home builders.
Give one reason why some homes have roofs which have a greater pitch.
There is less snow build up in the wintertime.
Engineers refer to the slope of a road as the grade.
They often refer to the slope as a percentage.
Slopes and Lines
rise
run
The slope of a line is the steepness of the line.
riseslope =
run
8 ft
100 ft
A grade of 8% would mean for every rise of 8 feet, there is a run of 100 feet.
8slope =
100
= 8%
The steepness of wheelchair ramps is of great importance to those who use them.
The slope of wheelchair ramps is usuallyabout 1 foot rise for every 12 feet of run.
1 ft12 ft
If the rise is 2 feet, what is the run?
Answer: 24 feet
3 m
5 m
Determine the slope (pitch) of the roof.
5
3m m
m
2
3m
3
3m
Determine the slope of the staircase.
23
33= 1
6 yd
3 secrise
runm
2
4 6 1080 12 14
4
6
8
10
12
2
Determine the slope.D
ista
nce
(ya
rds)
Time (seconds)
m = 6 yards 3 secondsm = 2 yds/sec
– 5
75
7m
rise
runm
Determine the slope.
2
4 6 1080 12 14
4
6
8
10
12
2
7
0
7m
rise
runm
0m
Horizontal lines have a slope of zero.2
4 6 1080 12 14
4
6
8
10
12
2
Determine the slope.
6 6
0m
rise
runm
(undefined)
Vertical lines have slopes which are undefined.
2
4 6 1080 12 14
4
6
8
10
12
2
Determine the slope.
cannot divide by zero!
rise
runm
positive
negative
zeroundefined
Summary: Types of Slopes
Slope MountainSki Resort
Positive slope, + work
Negative slope, - work
Zero slope is zero fun! Undefined
slope.
Oh No!!!!
T. Merrill 2005
Slope of line through 2 points
• To find the slope of a line through 2 given points we use the formula
• For example, Find the slope of a line that goes through (-3, 5) and (2, 18)
12
12
xx
yyslope
x1 y1 x2 y2
12
12
xx
yyslope
185 2-3
5
13
Determine the slope of this line.
5
40
riseslope =
run
40
5m = 8
How can you find slope when counting lines is just too much?
Let’s take a closer look . . .
(7, 70)
(2, 30)
Δx
Δy
In general,
(x2, y2)
(x1, y1)
Δx
Δy
Determine the slope of the line segment.
(20, 7)
(80, 5)x1 y1
x2 y2
Draw a line which has a slope of 1
2
Draw a line which has a slope of 2
Draw a line which has a slope of 5
6
–5
6
–5
6
What Type of Slope is Shown?
Positive Slope
Negative Slope
Zero Slope
No Slope/Undefined
Slope of a Table• In a table we can use the same formula. Pick any
two pairs in the table for coordinates
x y
-4 -17
1 -2
3 4
8 19
10 25
Pick any two rows. If it is linear it will be the same
no matter which two rows you pick
12
12
xx
yyslope
x1
x2
y1
y2 13
24
slope13
24
2
6 3
Conclusion
• Slope is:
• Describe the slope of each of the following
the rate of change of a line
run
riseslope
12
12
xx
yyslope
Negative slope Undefined/ No slope
Positive slope Zero/0 slope
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