8-7: parallel and perpendicular lines

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8-7: Parallel and Perpendicular Lines Mr. Gallo

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8-7: Parallel and Perpendicular Lines. Mr. Gallo. Parallel Lines. If two non-vertical lines have the _________ ________, then the lines are ___________. same. slope. parallel. The 2 lines to right, a and b are parallel and have a slope of 2. What is the equation for each line? a: b: . - PowerPoint PPT Presentation

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Page 1: 8-7: Parallel and Perpendicular Lines

8-7: Parallel and Perpendicular Lines

Mr. Gallo

Page 2: 8-7: Parallel and Perpendicular Lines

Parallel Lines If two non-vertical lines have the _________

________, then the lines are ___________.

5

4

3

2

1

-1

-2

-3

-4

-5

-6 -4 -2 2 4 6

a

b

The 2 lines to right, a and b are parallel and have a slope of 2.

What is the equation for each line?

a:

b:

same slopeparallel

2 1y x

2 2y x

Page 3: 8-7: Parallel and Perpendicular Lines

Examples: Write the slope of any line that is parallel to each given line.

1). 2.)    _________________

3 2y x 2 3 6x y

3mAB

m 23

23

Page 4: 8-7: Parallel and Perpendicular Lines

Point-Slope Form of an Equation:

1 1y y m x x

Where:slopey coordinate of a given point

x coordinate of a given point

Page 5: 8-7: Parallel and Perpendicular Lines

Write an equation in point-slope form for the line containing and parallel to .

1 1y y m x x

𝑚=¿ 𝑦1=¿ 𝑥1=¿¿3 4 3

1 1y y m x x

___ ___ ___y x 34 3

Page 6: 8-7: Parallel and Perpendicular Lines

Write an equation in point-slope form for the line containing and parallel to 6.

1 1y y m x x

𝑚=¿ 𝑦1=¿ 𝑥1=¿¿23

AB

1 3

1 1y y m x x

___ ___ ___y x 231 3

Page 7: 8-7: Parallel and Perpendicular Lines

Write an equation in point-slope form for the line containing and parallel to 6.

1 1y y m x x

𝑚=¿¿¿ 𝑥1=¿¿4 1undefined

The original line is vertical so a vertical line with the equation would be parallel.

Page 8: 8-7: Parallel and Perpendicular Lines

Perpendicular Lines If two non-vertical lines have

that are opposite , then the lines are perpendicular..

The 2 lines to right, a and b are perpendicular and have slopes of and 2 respectively.

What is the equation for each line?

a:

b:

slopesreciprocals

1 12

y x

2 2y x

5

4

3

2

1

-1

-2

-3

-4

-5

-6 -4 -2 2 4 6a

b

Page 9: 8-7: Parallel and Perpendicular Lines

Examples: Write the slope of any line that is perpendicular to each given line.

1). 2.)    _________________

3 2y x 2 3 6x y

13

m

23

m

32

m

Page 10: 8-7: Parallel and Perpendicular Lines

Write an equation in point-slope form for the line containing and perpendicular to .

1 1y y m x x

𝑚=¿ 𝑦1=¿ 𝑥1=¿¿

13 4 3

1 1y y m x x

___ ___ ___y x 4 313

Page 11: 8-7: Parallel and Perpendicular Lines

Write an equation in point-slope form for the line containing and perpendicular to 6.

1 1y y m x x

𝑚=¿ 𝑦1=¿ 𝑥1=¿¿32

1 3

1 1y y m x x

___ ___ ___y x 32

1 3

23

m

Page 12: 8-7: Parallel and Perpendicular Lines

Write an equation in point-slope form for the line containing and perpendicular to 6.

1 1y y m x x

𝑚=¿¿¿ 𝑥1=¿¿4 1

undefined

The original line is vertical so a horizontal line with the equation would be perpendicular.

0

Page 13: 8-7: Parallel and Perpendicular Lines

Homework: Reteach 8-7