6.6
description
Transcript of 6.6
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6.6
Parallel & Perpendicular Lines
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6.6 – Parallel & Perp. Lines
Goals / “I can….” Determine whether lines are parallel Determine whether line are perpendicular
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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
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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
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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
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Write an equation given the slope and y-interceptEXAMPLE 1
Write an equation of the line shown.
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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
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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.
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Parallel lines
Lines in the same plane that do not intersect are called parallel lines. Parallel lines have the same slope.
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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
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Parallel Lines
Determine if the lines are parallel
1.
2x + 6y = 12
6y = -2x + 12
yes
53
1 and1262 xyyx
23
1 xy
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Parallel Lines
Determine if the lines are parallel
2.
6x + 8y = -24
8y = -6x – 24
No
34
3 and 2486 xyyx
34
3 xy
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6.6 – Parallel & Perp. Lines
Given a line and another point, can you write a parallel line?
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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
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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
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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.
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Perpendicular Lines
Lines that intersect at right angles are called perpendicular lines. The slopes of these lines are opposite reciprocals.
Opposite reciprocals????
3…..
...41
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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
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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
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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
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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
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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
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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