6.6

Parallel & Perpendicular Lines

6.6 – Parallel & Perp. Lines

Goals / “I can….” Determine whether lines are parallel Determine whether line are perpendicular

Mini Quiz 45

1.Find the reciprocal of each fraction

a. b. c. d.

2.Find the slope and y-intercept of each equation

2

1

3

4

2

5

26 d.6 c.83

5b.4

4

5 a. xyxyxyxy

Quick Review/Preview

1. What is the Slope-Intercept Form?

y = mx + b

2. What is the Standard Form?

Ax + By = C

3. What is the Point-Slope Form?

y – y1 = m(x – x1)

4. Find the “negative reciprocal” of each fraction

3

4d.

2

1c.

7

3b.

5

2a.

4

32

1

2

3

7

2

5

Various Forms of an Equation of a Line.

Slope-Intercept Form

Standard Form

Point-Slope Form

slope of the line

intercept

y mx b

m

b y

, , and are integers

0, must be postive

Ax By C

A B C

A A

1 1

1 1

slope of the line

, is any point

y y m x x

m

x y

Write an equation given the slope and y-interceptEXAMPLE 1

Write an equation of the line shown.

GUIDED PRACTICE for Example 1

Write an equation of the line that has the given slope and y-intercept.

1. m = 3, b = 1

y = x + 13

ANSWER

2. m = –2 , b = –4

y = –2x – 4

ANSWER

3. m = – , b =

34

72

y = – x +34

72

ANSWER

6.6 – Parallel & Perp. Lines

Parallel lines are two lines that NEVER intersect.

Two lines are parallel if they have the SAME slope and different y-intercept.

Parallel lines

Lines in the same plane that do not intersect are called parallel lines. Parallel lines have the same slope.

6.6 – Parallel & Perp. Lines

Example: Are these two lines parallel?

y = -2x – 1 4x + 2y = 6 Since they are in different forms, you need

to switch them to the same form.

y = -2x – 1 2y = -4x + 6

2 2 2

y = -2x + 3

Parallel Lines

Determine if the lines are parallel

1.

2x + 6y = 12

6y = -2x + 12

yes

53

1 and1262 xyyx

23

1 xy

Parallel Lines

Determine if the lines are parallel

2.

6x + 8y = -24

8y = -6x – 24

No

34

3 and 2486 xyyx

34

3 xy

6.6 – Parallel & Perp. Lines

Given a line and another point, can you write a parallel line?

Equations of Parallel Lines

4. Write an equation for the line that contains

(5, 1) and is parallel to

m =

45

3 xy

5

3

55

31 xy

Equations of Parallel Lines

5. Write an equation for the line that contains

(2, -6) and is parallel to

m = 3

y + 6 = 3(x – 2)

93 xy

6.6 – Parallel & Perp. Lines

Perpendicular lines are lines that intersect to form a right angle.

Two lines are perpendicular if the product of their slopes is – 1. This means that the slopes are opposite reciprocals.

Perpendicular Lines

Lines that intersect at right angles are called perpendicular lines. The slopes of these lines are opposite reciprocals.

Opposite reciprocals????

3…..

...41

Perpendicular Lines

What is the slope of the perpendicular line?

7. -5/2

8.5/1 = 5

9.1/2

85

2 xy

xy5

1

72 xy

Equations of Perpendicular Lines

10. Find the equation of the line that contains (0, -2) and is perpendicular to y = 5x + 3

m = 5

1

xy5

12

Equations of Perpendicular Lines

11. Find the equation of the line that contains

(1, 8) and is perpendicular to

m =

14

3 xy

3

4

13

48 xy

Equations of Perpendicular Lines

12. Find the equation of the line that contains

(2, -3) and is perpendicular to

m = 2

y + 3 = 2(x – 2)

62

1 xy

Perpendicular Lines

13. Determine if the lines are perpendicular: and

No14. Determine if the lines are perpendicular:

and

Yes

42313

2 xyxy

93453

4 xyxy

423 xy423 xy

3

4

3

2 xy

934 xy934 xy

4

9

4

3 xy

Challenge

What is the slope of the line that is parallel to x = 4?

undefined What is the slope of the line that is

perpendicular to x = 4?

zero