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03.03 S KM & PP 1
Slope
03.03 S KM & PP 2
Definition: Slope
The slope of the linecontaining points
P1(x1, y1) and P2(x2, y2) is given by
21
12
12 xx,xxyy
m
The denominator
can’t be zero.
03.03 S KM & PP 3
A Slope Triangle
21
12
12 xx,xxyy
m
P1(x1, y1)
RUNx2 - x1
RISEy2 - y1
P2(x2, y2)
RISEy2 - y1
x2 - x1
RUN
03.03 S KM & PP 4
m
Slope
xy
21
12
12 xx,xxyy
m
xinchange
yinchange
RunRise
xdelta
ydelta
03.03 S KM & PP 5
Compute the Slope
(-2, -3)
(4, -1)
3
1
6
2
24
31
)(
m
upwards
03.03 S KM & PP 6
Another Slope
(-4, -3)
(0, 5)
21
2
4
8
40
35
m
upw
ards
03.03 S KM & PP 7
Compute this Slope
(-5, 2)
(4, -1)
3
1
9
3
54
21
)(
m
DOWNWARDS
03.03 S KM & PP 8
Compute the Slope
(-5, -1)
(4, -1)
0
9
0
54
11
)(
m
HORIZONTAL
03.03 S KM & PP 9
Compute the Slope
(-4, -5)
(-4, 0)
Undefined
)(m
0
5
44
50
VER
TIC
AL
03.03 S KM & PP 10
SLOPEBASICS
POSITIVE SLOPE The line rises from left to right.
ZERO SLOPE The line is HORIZONTAL (zero rise)
NEGATIVE SLOPEThe line falls from left to right.
UNDEFINED SLOPEThe line is VERTICAL (zero run)
03.03 S KM & PP 11
Practice Problem 1a
3
2
Determine the slope of the line
containing points P1 and P2. ),(P 571 ),(P 912
6
4
71
59
)(
m
RUN = 3
RISE = 2
The line rises from left to right.
03.03 S KM & PP 12
Practice Problem 1b
Determine the slope of the line
containing points P1 and P2. ),(P 531 ),(P 232
0
7
33
52
)(
m
The slope is undefined.
Vertical Line
03.03 S KM & PP 13
Practice Problem 1c
2
1
Determine the slope of the line
containing points P1 and P2. ),(P 301 ),(P 542
4
2
04
35
)(
m
RUN = 2
RISE = -1
The line falls from left to right.
03.03 S KM & PP 14
Practice Problem 1d
0
Determine the slope of the line
containing points P1 and P2. ),(P 571 ),(P 512
6
0
71
55
)(
m
RUN = 6RISE = 0
The line is Horizontal.
03.03 S KM & PP 15
That’s All for Now!
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