slopes (or steepness ) of lines are seen everywhere
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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. - PowerPoint PPT PresentationTRANSCRIPT
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
8100
A grade of 8% would mean for every run of 100 units, there is a rise of 8 units.
8slope =
100
= 8%
The steepness of wheelchair ramps is of great importance to handicapped persons.
1
12The slope of wheelchair ramps is usually about
112
If the rise is 1.5 m, what is the run?
Ans: 18 m
Determine the slope of the line.
5 cm
9 cm
5
9m
We use the letter m because in French the word for “to go up” is monter.
Because the slope is a ratio, there are no units such as cm or cm2.
3 m
5 m
Determine the slope (pitch) of the roof.
5
3m
2
3m
3
3m
1m
Determine the slope of the staircase.
23
3
3
3
9
3
9m
1
3m
rise
runm
2
4 6 1080 12 14
4
6
8
10
12
2
Determine the slope.
– 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 no slope.2
4 6 1080 12 14
4
6
8
10
12
2
Determine the slope.
rise
runm
positive
negative
zeroundefined
Summary: Types of Slopes
Determine the slope of this line.
Which points will you use to determine rise and run?
5
40 riseslope =
run40
5m
= 8
Determine the slope of the line segment.
60–2
2
60m
1
30
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
Draw a line which has a slope of …
–3
1–3
1
a) – 3 b) 3
3
13
1
3
9
3
9m
1
3m
rise
runm
2
4 6 1080 12 14
4
6
8
10
12
2
Remember this example?
9 6 3
13 4 9m
1
3m
rise
runm
2
4 6 1080 12 14
4
6
8
10
12
2
You can use the coordinates of two points on the line to find the slope.
4,6
13,9
Formula for Slope
When given the coordinates of two points on
the line: and
the slope is the difference of the y-coordinates divided by the difference of the x-coordinates.
To represent the difference, we use the Greek letter for d, delta, in the formula.
Slope = =
1 1,x y 2 2,x y
2 1
2 1
y y
x x
y
x
Summary
Slope = = =
y
x
rise
run2 1
2 1
y y
x x
Examples:
Find the slope of the line passing through the two points. Use your answer to decide whether the line is increasing, decreasing, vertical, or horizontal.
a) and
b) and
c) and 2, 3
1, 8
2, 3
2, 4
2, 3 2, 3
Answers:
a) decreasing
b) vertical
c) horizontal
3 3 00
2 2 4m
3 3 6
2 2 0m undefined
8 4 12
121 2 1
m