M. Pickens 2006
Slope
M. Pickens 2006
What is Slope?
Slope is the rate of change of a line
run
riseslope x
yslope
(change in y)
(change in x)
12
12
xx
yyslope
M. Pickens 2006
Slope of a Graph
1.First pick two points on the lineThe 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
riseslope
3
2
M. Pickens 2006
Slope of a Graph
1.First pick two points on the lineThe 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
riseslope
2
10 5
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)
12
12
xx
yyslope
X1 y1 X2 y2
12
12
xx
yyslope
185 2-3
5
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)
12
12
xx
yy
run
rise
98
27
1
9
12
12
xx
yy
47
42
59
14
3
2
47
42
59
14
4
3
X1 y1 X2 y2
9
X1y1 X2 y2
X1 y1 X2y2
3
2
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)
12
12
xx
yy
run
rise
51
20
4
2
12
12
xx
yy
33
31
44
22
0
2
33
31 Undefined, NO slope
44
220
8
0
X1 y1 X2 y2
2
1
X1y1 X2 y2
X1 y1 X2y2
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
12
12
xx
yyslope
x1x2
y1
y2 13
24
slope13
24
2
6 3
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
12
12
xx
yyslope
31
25.475.2
2
5.1
75.04
3
12
12
xx
yyslope
86
23
86
23
2
1
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
12
12
xx
yyslope
105
1710
105
1710
5
7
12
12
xx
yyslope
31
88
31
88
2
0 0
M. Pickens 2006
Conclusion
• Slope is:
• Describe the slope of each of the following
the rate of change of a line
run
riseslope
12
12
xx
yyslope
Negative slope Undefined/ No slope
Positive slope Zero/0 slope