2. Plot a point at
. Then go 1 unit up and 3 units to the right. This point is
. Draw a line through
these two points.
3. Plot a point at
. Then go 2 units down and 5 units to the right. This point is
. Draw a line
through these two points.
4. Plot a point at
. There is no rise in this equation’s graph. This implies the slope is 0 and is a
horizontal line at
.
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5. Plot a point at
. There is no run in this equation’s graph. This implies the slope is undefined and is a
vertical line at
x
= 2.
Comparing the Characteristics of Parallel and Perpendicular Lines
The following table is a summary of the characteristics you would observe when you graph lines that are either parallel or perpendicular.
Parallel lines
Perpendicular lines
everywhere equidistant
intersect at right angle
same slope
slope that are negative reciprocals of each other
For example, consider an equation such as
y
= 2
x
+ 3. One line parallel to this line would be
y
= 2
x
+ 5. Note that the coefficient of
x
is 2 for
both, since parallel lines have the same slope, but have different
y
intercepts.
A graph of these two equations is shown below.
Given the same equation
, one line perpendicular to this line would be
. Note that the slopes (the coefficient of
x
) of
the lines are 2 and
. The first slope is 2 and the second is the reciprocal of 2 with the opposite sign, giving
. To obtain the slope of a
line perpendicular to
, find the negative reciprocal of the
m
, which is
. A graph of these two equations is shown below.
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©; 2015 Connections Education LLC.
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- Winter '13
- Kramer
- Algebra, Equations, Slope, Related Slopes
