The document discusses parallel and perpendicular lines. It explains that parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other. The document provides examples of writing equations for lines that are parallel or perpendicular to given lines and pass through specific points. It also gives examples of determining whether two lines are parallel or perpendicular based on their slopes.

1. 5.5 Parallel and
Perpendicular Lines
SWBAT verbally tell me how the slope of parallel lines
and perpendicular lines are related. They can find the
equation of a line parallel/perpendicular to a given line
that passes through a given point.
http://apod.nasa.gov/apod/
The Dark Doodad Nebula

2. Mini Quiz 45
1.Find the reciprocal of each fraction
a.
1
2
b.
4
3
c.
1
−
3
d.
5
−
2
2.Find the slope and y-intercept of each equation
5
a. y = x + 4
4
5
b. y = x − 8
3
c. y = 6 x
d. y = 6 x + 2

3. 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
2
3 7
1 2
4 3
5
a.
b. −
c. −
−
= 2 d. −
5
7 3
2 1
3 4
2

4. Overview
Parallel Lines and Perpendicular Lines
 Property of their slopes
 Write equations for each type of lines


5. Parallel Lines
Parallel Lines - lines that never intersect
What is the slope of the
red line?
1/2
What is the slope of the
blue line?
1/2
Parallel Lines have the same slope!

6. Parallel Lines
Determine if the lines are parallel
1
1. 2 x + 6 y = 12 and y = − x + 5
3
2x + 6y = 12
6y = -2x + 12
1
y = − x+2
3
yes

7. Parallel Lines
Determine if the lines are parallel
3
2. 6 x + 8 y = −24 and y = x − 3
4
6x + 8y = -24
8y = -6x – 24
3
y = − x +3
4
No

8. Parallel Lines
Determine if the lines are parallel
2
3. 4 x + 6 y = −2 and y = x −8
3
4x + 6y = -2
6y = -4x – 2
2
1
y = − x−
3
3
No

9. Equations of Parallel Lines
4. Write an equation for the line that
3
contains (5, 1) and is parallel to y = x − 4
5
3
m=
5
3
y − 1 = ( x − 5)
5

10. Equations of Parallel Lines
5. Write an equation for the line that
contains (2, -6) and is parallel to y = 3x + 9
m=3
y + 6 = 3(x – 2)

11. Equations of Parallel Lines
6. Write an equation for the line that
1
contains (-4, 3) and is parallel to y = x + 7
2
1
m= 2
1
y − 3 = ( x + 4)
2

12. Perpendicular Lines
Perpendicular Lines – lines that intersect to form
right angles
What is the slope of the
red line?
-1/4
What is the slope of the
blue line?
4/1
Perpendicular Lines have negative reciprocal slope!

13. Perpendicular Lines
What is the slope of the perpendicular line?
2
7. y = x − 8
5
1
8. y = − x
5
9. y = −2 x − 7
-5/2
5/1 = 5
1/2

14. Equations of Perpendicular Lines
10. Find the equation of the line that
contains (0, -2) and is perpendicular to
y = 5x + 3
1
m=−
5
1
y+2=− x
5

15. Equations of Perpendicular Lines
11. Find the equation of the line that
contains (1, 8) and is perpendicular to
3
y = x+1
4
4
m =− 3
4
y − 8 = − ( x − 1)
3

16. Equations of Perpendicular Lines
12. Find the equation of the line that
contains (2, -3) and is perpendicular to
1
y = − x+ 6
2
m=2
y + 3 = 2(x – 2)

17. Perpendicular Lines
13. Determine if the lines are perpendicular:
2
y = x + 1 and 3 y + 2 x = 4
3
3y + 2x = 4
3 y = −2 x + 4
2
4
y =− x+
3
3
No
14. Determine if the lines are perpendicular:
4
y = x − 5 and 4 y + 3 x = 9
3
4y + 3 x = 9
4 y = −3 x + 9
y =−
3
9
x+
4
4
Yes