DEFINING SLOPE
SECTION 5.2
Slope
rise to
________
is the ratio of vertical ______
run
horizontal _____.
Slope =
rise
run
=
SLOPEMAN
My one
weakness is
that I can
only run to
the right.
Remember,
I can only
run to the
right!
If I run uphill, then
the slope of the line
is positive.
Rise
Run
Lines with a
positive
slope go
uphill from
left to right.
Slopeman is
going
UPHILL so
the slope is
POSITIVE.
Lines with
POSITIVE
slope go UP
from left to
right
If I run DOWNHILL,
then the slope of
the line is
NEGATIVE.
Lines with a
NEGATIVE
slope go
DOWN from
left to right.
Rise
Run
Remember,
I can only
run to the
right!
Slopeman is
going
downhill so
the slope is
negative.
EXAMPLE 1: Find the slope of the following lines.
rise
slope =
 2
run
2
Run
Rise
EXAMPLE 1: Find the slope of the following lines.
rise
3
slope =

run
1
1
3
EXAMPLE 1: Find the slope of the following lines.
rise
slope =
 1
run
2
1
2
Slope is positive.
1
m
2
Plot the following points on the graph and find the slope.
4
2
+2
x
y
4
1
6
5
difference in range
Slope is positive.
4
m 2
2
difference in domain

+4
+4

+2
2
Example 2: Find the slope between the following points without graphing.
-8
x
y
9
6
1
4
-2

-8
difference in domain
difference in range
-2
1

4
1
m
4
Example 2: Find the slope between the following points without graphing.
+6
x
y
-1
3
-6
5 -3
difference in range
difference in domain

-6
+6
 1
m  1
Example 2: Find the slope between the following points without graphing.
x
+45
y
-31
29
-81
14 -52
difference in range
difference in domain

-81   9
+45
5
9
m
5
Sometimes when you must find the slope of a line without having a picture of
the graph, it is easier to find the slope of a line using the following formula.
Slope =
y1  y 2
x1  x2
when the two points are
x1 , y1 
and
x2 , y 2 
Example 3:
Find the slope of the line containing the following points
9, 6
and 1, 4
64  2  1
9 1
8
1
m
4
4
Example 3:
Find the slope of the line containing the following points
 1,3
and 5, 3
3   3
1  5

6
6

m  1
1
Choose any two points on the line and find the slope of the line.
x y
-3
difference in range
difference in domain

+0
-3
4
3
1
3
m0
+0
If I tried to ski on
this line, how fast
would I travel?
zero miles per hour
The slope of any
horizontal line is
zero.
Choose any two points on the line and find the slope of the line.
x y
+0
difference in range
difference in domain

-4
+0
-2
1
-2
-3
-4
m  undefined
What would happen
if I tried to ski off
this vertical cliff?
HELP !!
I would have
UNDEFINED
body parts!!
The slope of any
vertical line is
undefined.