5.2
Defining Slope
Brian Preston
Algebra 1 2009-2010
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Real World Application
How steep is this hiking trail?
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Lesson Objectives
1) Find the slope of a line
using two of its points.
2) Use the slope and any
point on a line to write an
equation of the line.
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Review
1) 10 – ( – 7) = 17
2) – 3 – 4 =
– 7
3) – 5 + 9 =
4
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Review
5
4
3
2
1
-5 -4 -3
x
-2 -1
-1
1 2
3
4
5
-2
-3
-4
-5
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Definition
Slope – m
Rise
Slope –
Run
range of the Y-value
Slope –
range of the X-value
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What is range?
range of the Y-value
Slope –
range of the X-value
Range – Highest number minus
the Lowest number
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What does slope mean?
Run
Rise
Run
Rise
Run
Rise
Run
Rise
P
PRESTON
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What does slope mean?
P
PRESTON
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Real World Application
4) Yara & Nidal are hiking up a hill.
The run for Yara’s step is 32
inches, and the rise is 8 inches. The
run for Nidal’s step is 36 inches,
and the rise is 9 inches. Find the
slope of the lines representing each
hikers pathway up the hill.
1
9 – 8
range
H-L of the Y-value
range
H-L of the X-value
=
36 – 32
=
4
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Real World Application
5) The coordinate plane below shows the
position of a ladder resting against the side
of a barn. Find the slope of the ladder.
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Real World Application
5) The coordinate plane below shows the
position of a ladder resting against the side
of a barn. Find the slope of the ladder.
Rise
Run
– 6
=
+2
= – 3
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Definition
Slope –
Slope –
Slope –
Slope –
y2 – y 1
x2 – x 1
m
Rise
Run
range of the Y-value
range of the X-value
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Example
6) Find the slope of the line
containing the points
2 4 & Q(5,–
5 – 6
P(–– 2,4)
6).
(x22
,y2)
(x11
,y1)
( – 6) – ( 4 )
– 10
y2 – y1
=
=
( 5 ) – ( – 2)
x2 – x1
7
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Example
6) Find the slope of the line
containing the points
2 4 & Q(5,–
5 – 6
P(–– 2,4)
6).
(x11
,y1)
(x22
,y2)
( 4 ) – ( – 6)
10
y2 – y1
=
=
( – 2) – ( 5 )
x2 – x1
– 7
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Example
7) Graph the line containing
the point (– 2,3) and having
5
– 4
4
slope m =
+3
3
Always make
3 points -5 -4 -3
2
– 4
1
-2 -1
-1
+3
1 2
3
4
5
-2
-3
-4
-5
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Example
8) Graph the line containing
the points (– 3,4) and
5
(– 3,4)
4
(1,2)
(1,2).
3
2
(1,2)
1
-5 -4 -3 -2 -1
-1
1 2
3
4
5
-2
-3
-4
-5
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Example
9) Use the Coordinates of point R
and Point S to find the slope of the
5
horizontal line
4
shown below.
0
Rise
0
= 0 -5 -4 -3
=
+5
Run
ero
Special line
R
3
S
2
+5 1
-2 -1
-1
1 2
3
4
5
-2
-3
-4
-5
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Example
10) Use the Coordinates of Point J
and Point K to find the slope of the
5
vertical line
4
J
shown below.
– 5
0
3
2
1
Rise
– 5
=
-5 -4 -3 -2 -1
-1
0
Run
K
-2
u
defined
=
-3
-4
Special line
-5
1 2
3
4
5
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Example
11) Find the slope.
Rise = – 3
Run = 2
slope =
Rise
– 3
=
2
Run
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Example
12) Find the slope.
5
x-int = 3
4
3
y-int = – 2
2
Rise
1
slope =
Run -5 -4 -3 -2+2-1-1
-2
2
-3
=
-4
3
-5
+3
1 2
3
4
5
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Definition
8 ÷ 0 = undefined
nothing nothing
nothing nothing
nothing
nothing
nothing
nothing
nothing
Undefined means it
doesn’t work, because
we could put 0(nothing)
in the cup infinite times
and still not reach 8 oz.
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Key Points & Don’t Forget
1) A negative times a
negative is a positive.
– 3  – 5 = 15
–
2
2) Slope
= u defined
0
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The Assignment
pg. 231-232 #’s 11-19 odd,
20-42 even, 45, 47
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