Slopes of Perpendicular Lines

1. 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

2. Are these lines perpendicular?
PullPull

3. 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

4. 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

5. 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

6. 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

7. 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:
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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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8. 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.