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Slopes of Lines

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on 4 October 2013

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Transcript of Slopes of Lines

Key concept: The slope of a line containing two points with coordinates (x ,y ) and (x ,y )is given by the formula
3-3 Slopes of Lines
Slope of a line
Slope =
Vertical rise
Horizontal run
In a coordinate plane, the slope of a line is the ratio of the change along the y-axis to the change along the x-axis
1
2
2
1
m=
y -y
x -x
2
2
1
1
where x doesn't equal x .
1
2
The slope of a line indicates whether the line rises to the right, falls to the right, or is horizontal. The slope of a vertical line where x = x .
1
2
.
0
x
y
(
-1
, 2)
(
-3
, -2)
First use the
rise
run
From (-3, -2) to (-1, 2), go up 4 units and right 2 units
rise
run
=
4
2
or 2
method.
.
Use the slope method.
(
-4
, 0)
(
0
, -1)
Let (-4, 0) be (x ,y ) and (0, -1) be (x ,y ).
1
1
2
2
m=
y -y
x -x
1
1
2
2
m=
-1 - 0
0- (-4)
or
-
1
4
y
x
0
x
0
.
(
-3
, 5)
(
1
, 5)
m=
y -y
x -x
1
1
2
2
m=
5-5
-3- 1
m=
0
-4
or 0.
(
6
, -4)
.
(
6
, 3)
x
y
0
m=
y -y
x -x
1
1
2
2
m=
3- (-4)
6-6
m=
7
0
which is undefined
The slope of a line can be used to identify the coordinates of any point on the line. It can also be used to describe a rate of change. The
rate of change
describes how a quantity is changing over time.
Look at the lines l, m, and n. Lines l and m are parallel, and n is perpendicular to l and m. Lets find the slopes of these lines
.
.
.
.
x
y
0
slope of l
slope of m
slope of n
m=
-
3
5
m=
3
-
5
m=
5
3
Since lines l and m are parallel, their slopes are the same. Line n is perpendicular to lines l and m, and its slope is the opposite reciprocal of the slopes of l and m; the is, -3/5* 5/3= 1. These results suggest 2 important algebraic properties of parallel and perpendicular lines
Postulates:
3.2- Two nonvertical lines have the same slope if and only if they are parallel.
3.3- Two nonvertical lines are perpendicular if and only if the product of their slopes is -1.
Slope Formula
Slope Formula
Slope Formula
m
l
n
(0, 4)
(4, 2)
(5, 1)
(-3, 5)
(2, 2)
(1, -3)
.
.
y
.
.
.
.
What you'll learn
-Find slopes of different lines.
-Use slope to identify perpendicular and parallel lines.
Sarah Prosser
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