# 6.6 Parallel and Perpendicular Lines Parallel Lines: ### 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 slope intercept form for each line. a. b. c. Line 1: ___________________ Line 1: __________________ Line 1: _________________ Line 2: _________________ 3.

Line 2: ___________________ Line 2: __________________ 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  4

x x

  7 7

y

  1 2

x

 2

y y

   3  7  3  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 ___________________________________ a. 6.

The following pairs of lines are perpendicular to each other. With your group, write an equation in slope-intercept form of each line. b. c. Line 1: ________________ Line 2: ________________ 7.

Line 2: _________________ Line 2: _________________ 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. Line 1: _________________ Line 1: _________________ 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: Parallel:

y

 2

x

 5 ____________________ 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