Slope
Supplement 2
Find a slope
Graphing with Slope
Slope
Slope describes the direction of a line.
Guard against 0 in the
denominator
SlopeIf x1 x2, the slope of the line
through the distinct points (x1, y1) and (x2, y2) is
12
12
xx
yy
xinchange
yinchange
run
risem
Why is this
needed?
x-axis
y-axis
Find the slope between (-3, 6) and (5, 2)
RiseRun
-48
-12
= =
Find the slope between(-3, 6) and (5, 2)
12
12
xx
yym
)3()5(
)6()2(
m8
4
2
1
Find the Slope
(5, -2)
(11, 2)
(3, 9)
12
12
xx
yym
1
2 9
11 3m
Green
511
)2(22
m
Blue
3
2 9
5 3m
Red
7
8
3
2
11
2
Find the slope between (5, 4) and (5, 2).
12
12
xx
yym
)5()5(
)4()2(
m0
2 STOP
This slope is undefined.
x-axis
y-axis
Find the slope between (5, 4) and (5, 2).
RiseRun
-20
Undefined= =
Find the slope between(5, 4) and (-3, 4).
12
12
xx
yym
)5()3(
)4()4(
m8
0
STOP
This slope is zero.
x-axis
y-axis
Find the slope between (5, 4) and (-3, 4).
RiseRun
0-8
Zero= =
From these results we can see...
• The slope of a vertical line is undefined.
• The slope of a horizontal line is 0.
x-axis
y-axis
Graph the line that goes through (1, -3) with
(1,-3)
4
3m
Using Slope to Graph
• Graph the line that contains (4, 5) and has a slope of 3/2.
(4, 5)
(6, 8)
(8, 11)
Using Slope to Graph
• Graph
(0, 8)
(4, 5)
(8, 2)
38
4y x
Slope Worksheet 10 points
Find the slope of the lines that contain the following pairs of points.
a. (2, 3) and (-4, -5)
b. (0, 0) and (2, 3)
c. (3, 0) and (7, 4)
d. (7, 4) and (3, 0)
e. (2, 3) and (2, -5)
Sketch a graph of the following lines.
1. y = 4x – 8
2. y = -3x + 6
3.
4.
5.
38
4y x
26
3y x
12
5y x
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