6.6 Parallel and Perpendicular Lines
1.
Write the definition and draw a diagram for each:
Parallel Lines:
Perpendicular Lines:
2.
The following pairs of lines are parallel to each other. With your group, write an equation in slopea. intercept form for each line.
b. c.
Line 1: ___________________
Line 2: ___________________
Line 1: __________________
Line 2: __________________
Line 1: _________________
Line 2: _________________
3.
Examine the slopes within each example above. Discuss with your group a pattern you see between the slopes of parallel lines. If two equations are in slope-intercept form, how can you tell if the lines are parallel?
4.
Given two equations. In the space provided state if the two lines are parallel or not parallel. (Hint: Make sure they’re in the correct form to see the slope!) y

3 x

5 y

3 x

7 _______________________ y

1
2 x

2 y y

3
4 x
 x


4

7
7 y
 
1
2 x

2 y y



3

3
7
 
4
4 x x
_______________________
_______________________
_______________________

5.
Work in your group to create your own equation of a line that would be parallel to each of the given equations. y

2 x

5 y
 
2
5 x
__________________________________
___________________________________________________
2 y

3 x

7 ___________________________________
6.
The following pairs of lines are perpendicular to each other. With your group, write an equation in slope-intercept form of each line. a. b. c.
Line 1: ________________
Line 2: ________________
Line 1: _________________ Line 1: _________________
Line 2: _________________ Line 2: _________________
7.
In your groups discuss the relationship between the slopes of two lines that are perpendicular to each other. Pay special attention to the slope and the two things that change . Develop a rule that communicates how to find the slope of a line that is perpendicular to a line with an equation given in slope-intercept form.
8.
Below are four equations. What would the slope be of a line that is perpendicular to these equations?
Equation y

2 x

5
Perpendicular slope
_____________ y

1
3 x y
 
3
4 x

7
_____________
_____________
3 y

7

2 x _____________

9.
Given the two equations below, write an equation of a line perpendicular to the given equations and a line parallel to the given equations.
Equation: y

2 x

5
Parallel: ____________________
Perpendicular: ____________________ y
 
2
3 x

7
_____________________
_____________________
10.
Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
(Remember: what form does the equation need to be in to see the slopes?) a.
y
3 x



3
2
2 y x

2

12 b. y
5 x
 
1
2

10 y x


3
2
15 c. y
4 x

3

4
3 x y


2
6