perpendicular lines – In a plane, any two oblique lines the product of whose slopes is -1.

Slopes of Perpendicular Lines

Remember Slope-Intercept Form of a Line?

y = mx + b

m = slope (rise over run)

b = y-intercept

y = mx + b

Are these lines perpendicular?

PullPull

Are the following slopes perpendicular?

Slopes Perpendicular?

No, the slopes have opposite signs, but are not reciprocals.

Are the following lines are perpendicular?

y = 4x + 2 y = –4x – 2

m1 = 4 m2 = –4

Answer

Slope of Line 2Slope of Line 1

Are the following lines are perpendicular?

Yes, the slopes are opposite reciprocals.Answer

Slope of Line 2Slope of Line 1

Are the following lines are perpendicular?

Yes, the slopes are opposite reciprocals. The y-intercept is not important for perpendicularityAnswer

Slope of Line 2Slope of Line 1

Are the following lines are perpendicular?

No, the slopes are reciprocals, but do not have opposite signs. Answer

Slope of Line 1 Slope of Line 2

Original Slope Perpendicular Slope

Find the Perpendicular Slope

Now that we have defined perpendicular lines, find five examples of perpendicular lines in the classroom. For each example, explain why it is important that the lines are perpendicular, if it is not important, explain why not.

Lesson objectives Teachers' notes

1) Learn the definition of perpendicular lines

2) Determine whether the slopes of two lines are perpendicular.

3) Determine whether two lines in slope-intercept form are perpendicular.

4) Find the perpendicular slope to a given slope.

Slopes of Perpendicular Lines

Teachers' notesLesson objectives

Subject:

Topic:

Grade(s):

Prior knowledge:

Cross-curricular link(s):

Mathematics

Perpendicular Slope

Algebra 1 or Algebra 2

Slope-Intercept Form of a line. Finding slope of a line given its graph.

Find perpendicular lines in the classroom.

Lesson notes:

Next Page

Common Core Standard - G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

Teachers' notesLesson objectives

Lesson notes (continued):

1) The book's definition of perpendicular lines is given. Redefine after student discovery.

2) Refresh student memory on Slope-Intercept Form. Stress that m & b are independent.

3) Refresh student memory on graphs of lines. Refresh memory on how to count slope.

4) Use the protractor to show that lines are perpendicular. Lead students on a discovery of what perpendicular pairs look like.

5) Have students determine why or why not pairs represent perpendicular slopes.

6-9) Have students find the slopes of both lines and determine why or why not the lines are perpendicular. Stress that the y-intercepts are not important for this determination.

10) Have students find the perpendicular pair given an original slope.

11) Have students find examples of perpendicular lines in the classroom. Have the students determine why or why not the examples need to be perpendicular.

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Page(s) Associated Notes

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Teachers' notesLesson objectives

Lesson notes (continued):

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Source Credits

Page 1 - definition from "Algebra 2" by Holliday, et. at., Glencoe, 2005.

Page 3 - Interactive software from Smart Technologies Smart Notebook 10.

Page 4 - Graphics and protractor from Smart Technologies Smart Notebook 10.