Parallel And Perpendicular Lines Worksheet Page 17
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50c.
d.
y
y
( 6,
)
( 3,
)
( 1,
)
3
5
5
Study Tip
x
O
Common
O
x
Misconception
( 6,
4)
A line with a slope of 0
is a horizontal line. The
slope of a vertical line is
y
y
y
y
2
1
2
1
m
m
undefined.
x
x
x
x
2
1
2
1
5
5
3
(
4)
3
1
6
6
0
7
or 0
, which is undefined
4
0
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.
Use Rate of Change to Solve a Problem
Example
Example
2
2
RECREATION
Between 1990 and 2000, annual sales of inline skating equipment
increased by an average rate of $92.4 million per year. In 2000, the total sales
were $1074.4 million. If sales increase at the same rate, what will the total sales
be in 2008?
Let (x
, y
)
(2000, 1074.4) and m
92.4.
1
1
y
y
2
1
m
Slope formula
x
x
2
1
y
10
7
4
.4
2
92.4
m
92.4, y
1074.4, x
2000, and x
2008
1
1
2
2
0
08
2
0
0
0
y
1074.4
2
92.4
Simplify.
8
739.2
y
1074.4
Multiply each side by 8.
2
y
1813.6
Add 1074.4 to each side.
2
The coordinates of the point representing the sales for 2008 are (2008, 1813.6).
Thus, the total sales in 2008 will be about $1813.6 million.
PARALLEL AND PERPENDICULAR LINES
m
y
n
( 0, 4 )
m
n
Examine the graphs of lines ,
, and
. Lines and
( 3, 5 )
m
n
m
are parallel, and
is perpendicular to
and
.
( 4, 2 )
( 5, 1 )
Let’s investigate the slopes of these lines.
( 2, 2 )
m
n
slope of
slope of
slope of
O
x
2
5
1
4
2
(
3)
m
m
m
2
(
3)
5
0
4
1
( 1,
3 )
3
3
5
5
5
3
m
n
Because lines and
are parallel, their slopes are the same. Line
is perpendicular
m
m
to lines and
, and its slope is the opposite reciprocal of the slopes of and
; that
3
5
is,
1. These results suggest two important algebraic properties of parallel
5
3
and perpendicular lines.
140 Chapter 3 Parallel and Perpendicular Lines
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