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Question 78908: How Do I determine which two equations represent perpendicular lines.
(a) y = 2x – 9 (b) y = x + 9 (c) y = - x + 9 (d) y = x - 9
I'm lost on which one!
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given the four equations:
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(a) y = 2x – 9
(b) y = x + 9
(c) y =- x + 9
(d) y = x - 9
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Note that all four equations are in the slope-intercept form. And the slope-intercept
form says that the slope of the graph equals the multiplier of the x in the equation.
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Here's the important part. For two lines to perpendicular to each other, they must have
slopes that are the negative inverse of each other. For example, if one has a slope of
+5, the perpendicular must have a slope of -1/5. If one has a slope of -9 the other must
have a slope of +1/9. If one has a slope of 5/6, the other must have a slope of -6/5. If
one has a slope of -7/9, the other has a slope of +9/7.
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That's the idea. Now let's look at the four equations and identify their slopes and the
negative inverse of their slopes. (Note again that the slope equals the multiplier
of the x in the equation.):
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Equation (a) slope = +2 and negative inverse of slope = -1/2
Equation (b) slope = +1 and negative inverse of slope = -1/1 = -1
Equation (c) slope = -1 and negative inverse of slope = -1/(-1) = +1
Equation (d) slope = +1 and the negative inverse of slope = -1/1 = -1
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Note that the graph of (a) does not have a line that is perpendicular to it because
the equation of any line perpendicular to (a) would need a slope of -1/2.
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How about equation (b)? Any line perpendicular to it would need to have a slope of -1.
Note that the graph of (c) has a slope of -1. Therefore the graphs of equations (b) and (c)
are perpendicular.
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How about equation (c)? Its graph has a slope of -1, so any graph that is perpendicular
to it will have a slope of +1. We already know that (b) has a slope of +1 and is, therefore,
perpendicular to (c). But what about (d)? Its graph has a slope of +1 also, so its graph
is also perpendicular to the graph of (c).
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So you have two pairs whose graphs are perpendicular ... (b) and (c) plus (c) and (d).
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Note also that this implies that (b) and (d) are parallel because they are both perpendicular
to a common line. (They also both have the same slope which is another way of telling
that they are parallel.)
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Hope this helps you to understand the problem a little better.
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