2. M. Pickens 2006
Objectives
• To learn what slope is
• To learn what a line looks like when it
has positive, negative, zero or undefined
slope
• To learn how to find the slope of a graph
• To learn how to find the slope given 2
points
• To learn how to find the slope of a table
3. M. Pickens 2006
What is Slope?
Slope is the rate of change of a line
run
rise
slope x
y
slope
(change in y)
(change in x)
1
2
1
2
x
x
y
y
slope
4. M. Pickens 2006
What does the line look like when…
• You have positive slope?
• You have negative slope?
• You have zero slope?
• You have NO slope?
5. M. Pickens 2006
Slope
Mountain
Ski Resort
Positive
slope,
+ work
Negative
slope,
- work
Zero
slope is
zero fun!
NO
slope.
Oh No!!!!
T. Merrill 2005
7. M. Pickens 2006
What Type of Slope is Shown?
Positive Slope
Negative Slope
Zero Slope
No Slope/Undefined
8. M. Pickens 2006
Slope of a Graph
• When slope is positive or negative we
need to find the actual value of the
slope or rate of change
• On a graph we find slope using the
formula
run
rise
slope
How far up or down it changes
How far left or right it changes
9. M. Pickens 2006
Slope of a Graph
1.First pick two points
on the line
The points need to be
where the lines cross
so they are integers
2. Then find the rise
and run
3. Determine if the
slope of the line is
positive or negative
Rise = 2
Run = 3
run
rise
slope
3
2
10. M. Pickens 2006
Slope of a Graph
1.First pick two points
on the line
The points need to be
where the lines cross
so they are integers
2. Then find the rise
and run
3. Determine if the
slope of the line is
positive or negative
Rise = 10
Run = 2
run
rise
slope
2
10
5
11. M. Pickens 2006
Slope of a Graphed Line
Find the slope of each
line below
x
y
Slopes:
RUN
RISE
1
1
4
4
4
4
Find the slope of each line below
0
6
0
1
4
2
8
4
3
undefined
0
2
12. M. Pickens 2006
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)
1
2
1
2
x
x
y
y
slope
X1 y1 X2 y2
1
2
1
2
x
x
y
y
slope
18
5 2
-3
5
13
13. M. Pickens 2006
Given two points on a line, find the slope:
1. (9, 2), (8, -7)
2. (-4, 4), (-7, 2)
3. (5, -1), (9, -4)
1
2
1
2
x
x
y
y
run
rise
9
8
2
7
1
9
1
2
1
2
x
x
y
y
4
7
4
2
5
9
1
4
3
2
4
7
4
2
5
9
1
4
4
3
X1 y1 X2 y2
9
X1
y1 X2 y2
X1 y1 X2
y2
3
2
14. M. Pickens 2006
Given two points on a line, find the slope:
4. (5, 2), (1, 0)
5. (3, -3), (3, -1)
6. (-4, -2), (4, -2)
1
2
1
2
x
x
y
y
run
rise
5
1
2
0
4
2
1
2
1
2
x
x
y
y
3
3
3
1
4
4
2
2
0
2
3
3
3
1 Undefined, NO slope
4
4
2
2
0
8
0
X1 y1 X2 y2
2
1
X1
y1 X2 y2
X1 y1 X2
y2
15. M. Pickens 2006
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
1
2
1
2
x
x
y
y
slope
x1
x2
y1
y2
1
3
2
4
slope
1
3
2
4
2
6
3
16. M. Pickens 2006
Slope of a Table
• Find the slope for each table below
x y
-3 4.25
-1 2.75
0 2
1 1.25
5 -1.75
x y
-8 2
-6 3
-3 4.5
-1 5.5
0 6
1
2
1
2
x
x
y
y
slope
3
1
25
.
4
75
.
2
2
5
.
1
75
.
0
4
3
1
2
1
2
x
x
y
y
slope
8
6
2
3
8
6
2
3
2
1
17. M. Pickens 2006
Slope of a Table
• Find the slope for each table below
x y
-10 17
-5 10
-1 4.4
5 -4
10 -11
x y
-3 -8
-1 -8
0 -8
1 -8
4 -8
1
2
1
2
x
x
y
y
slope
10
5
17
10
10
5
17
10
5
7
1
2
1
2
x
x
y
y
slope
3
1
8
8
3
1
8
8
2
0
0
18. M. Pickens 2006
Conclusion
• Slope is:
• Describe the slope of each of the following
the rate of change of a line
run
rise
slope
1
2
1
2
x
x
y
y
slope
Negative slope Undefined/
No slope
Positive slope Zero/0 slope
