Teaching Notes 4.9: Identifying Parallel and
Perpendicular Lines, Given an Equation
Identifying parallel and perpendicular lines when given an equation is relatively easy. A common
mistake arises from not understanding how the slopes of lines are related.- Draw and label the lines ofy= 3 x+1andy= 3 x−2 on the same graph as an example for
your students. Explain that these lines are parallel because the distance between them does
not change. Note that the slope of each line is 3. Emphasize that if two lines have the same
slope, they are parallel. - Draw and label the lines ofy=−
1
3
x+1andy= 3 x−2 on the same graph. Explain that
these lines are perpendicular because they intersect at right angles. Ask your students how
the slopes of the lines are related. (3 and1
3
are reciprocals; 3 and−1
3
have opposite signs.)
Explain that if two lines have slopes that are reciprocals and have opposite signs, the lines
are perpendicular. If necessary, provide more examples.- Provide an example of the graph of the intersection of a vertical line and a horizontal line,
such asy=3andx=2. Note that these two lines are perpendicular because each line is
parallel to an axis (y=3isparalleltothex-axis andx=2 is parallel to they-axis) and the
axes are perpendicular. - Review the information about parallel and perpendicular lines on the worksheet with your
students.
EXTRA HELP:
Be sure that the equation is in slope-intercept form so that you may easily identify the slope. If
the equation is not written in slope-intercept form, rewrite it.ANSWER KEY:
(1)Parallel (2)Perpendicular (3)Neither (4)Perpendicular (5)Parallel (6)Perpendicular
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(Challenge)Cheryl’s conclusion is incorrect. The lines are not perpendicular. If they were, the slopes
would have opposite signs (which they do), but the slopes would also be reciprocals.
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