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