Post on 31-Dec-2015
Write Equations of Parallel and Perpendicular lines
Section 5.5
#37 "Arithmetic is being able to count up to twenty without taking off your shoes."
-- Mickey Mouse
The Concept
In Chapter 4 we learned that parallel lines have slopes that are equal but have different y-intercepts
Today we’re going to learn about writing parallel line equations and also about perpendicular lines
In order to work through today’s lesson, we’ll be drawing heavily on our work with writing equations in slope intercept form
Parallel Lines In Chapter 4 we discussed the concept that lines that
have the same slope but different y-intercepts Based on this rule, if we are asked to write an
equation for a line parallel to another line, we simply “steal” it’s slope
For example if we wanted to write an equation for a line that goes through the point (-3,3) and is parallel to the line y=-2x+1
b
b
b
bxy
bmxy
3
63
)3(23
)(2
32 xy
PracticeWhat is the equation of the line parallel to the one given
and goes through the listed point
2 2;(1,3)y x
512 2
. 2 5
. 2 1
. 2 1
.
A y x
B y x
C y x
D y x
PracticeWhat is the equation of the line parallel to the one given
and goes through the listed point
12; (12, 3)
4y x 1
4
14
5114 4
. 6
. 4 51
.
.
A y x
B y x
C y x
D y x
PracticeWhat is the equation of the line parallel to the one given
and goes through the listed point
53; (1, 2)
6y x 5 17
6 6
5 76 6
5 26 3
5 76 6
.
.
.
.
A y x
B y x
C y x
D y x
Y
X
Y
X
Y
X
Y
X
Perpendicular lines In order to understand perpendicular lines, we must
first analyze the relationship between their slopes
m=-1
m=2
m=-1/2
m=1
PracticePlease give the slope of a line and perpendicular to the
given line
2 2y x
12
12
.2
. 2
.
.
A
B
C
D
PracticePlease give the slope of a line and perpendicular to the
given line
12
4y x
14
14
.4
. 4
.
.
A
B
C
D
PracticePlease give the slope of a line and perpendicular to the
given line
3 4y x
13
13
.3
. 3
.
.
A
B
C
D
PracticePlease give the slope of a line and perpendicular to the
given line5
36
y x 56
56
65
65
.
.
.
.
A
B
C
D
Perpendicular Lines• Now that we’ve established that the slopes of
perpendicular lines are negative reciprocals of each other, if we are asked to write an equation for a line parallel to another line, we simply “steal” it’s slope and modify it
For example if we wanted to write an equation for a line that goes through the point (-4,3) and is perpendicular to the line y=-2x-3
b
b
b
bxy
bmxy
5
23
)4(2
13
)(2
1
52
1 xy
PracticeWhat is the equation of the line perpendicular to the one
given and goes through the listed point
2 2;(2,3)y x
12
12
. 2 7
. 2 1
. 4
. 2
A y x
B y x
C y x
D y x
PracticeWhat is the equation of the line perpendicular to the one
given and goes through the listed point
12; ( 2, 3)
4y x 51
4 2.
. 4 51
. 4 5
. 4 11
A y x
B y x
C y x
D y x
PracticeWhat is the equation of the line parallel to the one given
and goes through the listed point
43; (2, 2)
7y x 7 11
4 2
374 2
374 2
1574 4
.
.
.
.
A y x
B y x
C y x
D y x
Most Important Points What’s the most important thing that we can learn
from today? Two lines are parallel if they have the same slope but with
different y-intercepts Perpendicular lines have slopes that are the negative
reciprocals of each other
Bellwork Solution Are these two lines parallel? Be prepared to
Explain y-2=2x & 2x+y=7
22
22
xy
xy
72
72
xy
yx
m=2 m=-2
.
.
A Parallel
B Not Parallel
Bellwork Solution Are these two lines parallel? Be prepared to
Explain -x=y+4 & 3x+3y=5
4
4
4
xy
xy
yx
35
533
533
xy
xy
yx
m=-1 m=-1.
.
A Parallel
B Not Parallel
Homework
5.5 Exercises1-8, 12-22, 27, 28, 32-34, 36, 38-42
Practical Example
Definitions
Perpendicular Two lines that intersect at a 90 degree
angle