4'5 The Slope of a Line

1
4.5 The Slope of a Line

• Goal Find the slope of a line.

2
Find the slope of the line below.
y
rise
Slope (m)

run
1
Slope (m)

x
3
3
1
1
m

3
3
Find the slope of the line below.
y
rise
Slope (m)

run
2
3
Slope (m)

2
3
x
3
m

2
4
Find the slope of the line below.
y
rise
Slope (m)

run
-1
Slope (m)

-1
4
x
4
-1
m

4
5
Find the slope of the line below.
y
rise
Slope (m)

run
-4
Slope (m)

2
x
-4
-2
m
2
6
Algebraic Method to Find Slope Given Two Points
Find the slope between (-1,3) and (4,7).
y2- y1
1
2
Slope (m)

x2- x1
7 - 3
m

4 (-1)
4
m

5
4
m
5
7
Algebraic Method to Find Slope Given Two Points
1
2
Find the slope between (6,5) and (-1,7).
y2- y1
m
x2- x1
7 - 5
m

-1 - 6
2
m

-7
-2
m
7
8
Algebraic Method to Find Slope Given Two Points
2
1
Find the slope between (-8,7) and (4,1).
y2- y1
m
x2- x1
7 - 1
m

-8 - 4
6
m

-12
-1
m
2
9
Slope of Horizontal and Vertical Lines
Horizontal Lines
Vertical lines
x -3
y 2
m undefined
m 0
x -3
y
y
y 2
x
x
10
Slope of Horizontal and Vertical Lines
Horizontal Lines
Vertical lines
(-3,2) (-3, -1)
(-2,2) (1,2)
x -3
y
y
(-2,2)
(1,2)
(-3,2)
y 2
x
x
(-3,-1)
11
Slope of Horizontal and Vertical Lines
Horizontal Lines
Vertical lines
(-3,2) (-3, -1)
(-2,2) (1,2)
1
2
1
2
y2- y1
y2- y1
m
m
x2- x1
x2- x1
2 - 2
-1 - 2
m
m
1 - -2
-3 - -3
-3
0
m
m
3
0
Watch Out!
m undefined or there is no slope
m 0
m 0 for all Horizontal Lines
m undefined for all Vertical Lines