6.6 Parallel and Perpendicular Lines Parallel Lines:

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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

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