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PARALLEL AND PERPENDICULAR LINES……

PARALLEL AND PERPENDICULAR LINES……. Slopes…… Parallel Lines: The slopes are EQUAL for parallel lines. Perpendicular Lines: The slopes are opposite reciprocals

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PARALLEL AND PERPENDICULAR LINES……

Slopes……

• Parallel Lines:

The slopes are EQUAL for parallel lines.

• Perpendicular Lines:

The slopes are opposite reciprocals for perpendicular lines.

mmll m

m1

Example……If

• PARALLEL:

• PERPENDICULAR:3

2m

3

2mmll 2

31 m

m

You Try.......

• If

find the parallel and perpendicular slopes.

• Parallel:

• Perpendicular:

2

1m

2

1m

2

1llm

2m

You Try……

• If

find the parallel and perpendicular slopes.

13

7m

Answer……Remember

• Parallel: • Perpendicular:

13

7m

13

7llm

7

13m

Example……

• A. What is the slope of ?

• B. What is the parallel slope?

• C. What is the perpendicular slope?

• A.

• B.

• C.

14

3 xy 4

3m

4

3llm

3

4m

Example……

• Graph the line parallel to through (8,2). 14

3 xy

Answer…..Parallel to 14

3 xy

4

3m

4

3llm

44

3

64

32

)8(4

32

)( 11

xy

xy

xy

xxmyy ll

Graph …….

14

3 xy 4

4

3 xy

Example…….

• Graph the line perpendicular to

through (3,2)

14

3 xy

Answer…Perpendicular to 14

3 xy

4

3m

63

4

43

42

)3(3

42

)( 11

xy

xy

xy

xxmyy

3

4m

Graph……

14

3 xy 6

3

4 xy

Are the following lines parallel, perpendicular, or neither?..........

• Answer:

• They have the same slope so they are parallel.

63

53

xy

xy

Parallel, Perpendicular, or Neither?

• The slopes are not the same so they are NOT parallel.

• The slopes are not opposite reciprocals so they are NOT perpendicular.

• They are neither.

62

72

xy

xy

Parallel, Perpendicular, or Neither?......

• You must first change both into slope-intercept form.

• Now, you can compare their slopes.

1896

632

yx

yx

23

2

623

632

xy

xy

yx

23

29

18

9

6

1869

1896

xy

xy

xy

yx

• They are not the same so they are NOT parallel.

• They are not opposite reciprocals so they are NOT perpendicular.

• They are neither.

3

2

3

2

2

1

Line

Line

m

m

Parallel, Perpendicular, or Neither?.....

• Change to slope-intercept form first.

• Compare their slopes.

18129

1234

yx

yx

43

4

1243

1234

xy

xy

yx

2

3

4

312

18

12

9

18912

18129

xy

xy

xy

yx

• The slopes are opposite reciprocals so they are perpendicular.

4

3

3

4

2

1

Line

Line

m

m

Assignment……• Worksheet