6.6 parallel & perpendicular lines. 6.6 – parallel & perp. lines goals / “i can….”...
TRANSCRIPT
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