Slope

1
Slope

• Rise over Run

2
Slope is defined as rise over run.
3 feet
6 feet
rise
3 feet
1

Slope

run
6 feet
2
3
Slope is defined as rise over run.
8 cm
2 cm
rise
8 cm
4

Slope

4
run
2 cm
1
4
Slope is defined as fall over run.
In this case, the slope is negative.
3 in
9 in
fall
-3 in
1
-

Slope
run
9 in
3
5
Slope is defined as fall over run.
In this case, the slope is negative.
1 m
4 m
fall
-1 m
1
-

Slope
run
4 m
4
6
Practice Time
7
Determine the slope of each ray.
8
1)
9
1)
24
12

2 units
4 units
10
2)
11
2)
53
23
1

5 units
3 units
12
3)
13
3)
33
1

3 units
3 units
14
4)
15
4)
27
2 units
7 units
16
5)
17
5)
-2 6
-1 3

6 units
2 units
18
6)
19
6)
-4 3
13
-1

3 units
4 units
20
7)
21
7)
-3 4
4 units
3 units
22
8)
23
8)
22
1
2 units
2 units
24
9)
25
9)
24
12

2 units
4 units
26
10)
27
10)
-3 7
7 units
3 units
28
11)
9
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-1
-2
-3
-4
-5
-6
-7
-8
-9
29
11)
44
1
9
8
7
6
5
4
3
4 units
2
1
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-1
-2
4 units
-3
-4
-5
-6
-7
-8
-9
30
12)
9
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-1
-2
-3
-4
-5
-6
-7
-8
-9
31
12)
-4 5
9
8
7
6
5
4
3
2
1
5 units
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-1
-2
-3
4 units
-4
-5
-6
-7
-8
-9
32
What is the slope of this line?
33
A horizontal line has a slope of zero.
rise
0

Slope
0
run
2
0 units
2 units
34
What is the slope of this line?
35
A vertical line has no slope. Its slope is
undefined.
rise
You cannot divide by zero.

Slope
?
run
0
36
Draw a line that has the given slope.
37
1) Slope
35
38
1) Slope
35
39
2) Slope
4
40
2) Slope
4
41
3) Slope
-2 3
42
3) Slope
-2 3
43
4) Slope
-1 6
44
4) Slope
-1 6
45
5) Slope
-3
46
5) Slope
-3
47
6) Slope
0
48
6) Slope
0
49
The slope of a line can be found by determining
the change in y values over the change in x
values.
7
6
5
(4,5)
4
3
2
(2,2)
1
0
1
2
3
4
5
6
7
8
9
10
50
The slope of a line can be found by determining
the change in y values over the change in x
values.
7
6
5-24-2
32

5
(4,5)
4
3
2
(2,2)
1
0
1
2
3
4
5
6
7
8
9
10
51
The slope of a line can be found by determining
the change in y values over the change in x
values.
7
(1,6)
6
6-21-5
4-4

-1
5
4
3
(5,2)
2
1
0
1
2
3
4
5
6
7
8
9
10
52
Use the two given points to determine the slope
of the line.
53
1)
y
(2,4)
(-3,1)
x
54
1)
y
(2,4)
(-3,1)
x
1-4-3-2
-3-5
35


55
2)
y
(-4,2)
x
(3,-3)
56
2)
y
(-4,2)
x
(3,-3)
2 (-3)-4 3
5-7
57


-
57
3)
y
(4,3)
(-2,-1)
x
58
3)
y
(4,3)
(-2,-1)
x
3 (-1)4 (-2)
46
23


59
4)
y
(1,5)
x
(-6,0)
60
4)
y
(1,5)
x
(-6,0)
5 01 (-6)
57

61
5)
y
(-5,3)
x
(2,-2)
62
5)
y
(-5,3)
x
(2,-2)
3 (-2) -5 2
5-7
57


-
63
6)
y
(0,0)
x
(2,-5)
64
6)
y
(0,0)
x
(2,-5)
0 (- 5) 0 2
5-2
52


-
65
7)
y
(0,6)
(5,4)
x
66
7)
y
(0,6)
(5,4)
x
6 4 0 5
2-5
25


-
67
8)
y
(0,6)
(5,0)
x
68
8)
y
(0,6)
(5,0)
x
6 0 0 5
6-5
65


-