Parallel and Perpendicular Lines
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Mathematics problems often deal with parallel and perpendicular lines.
Since these are such popular lines, it is important that we remember
some information about their slopes.

Parallel Lines:  (same slope!)

Parallel lines are marked with "feathers" to show that they are parallel.
These "feathers" look like "greater than" symbols.

Parallel lines have the same slope.

The symbol to indicate parallel lines is two vertical bars.
It looks something like the number 11.


where l1 and l2 are lines
m1 and m2 are slopes

   y = 3x + 5
   y = 3x - 7
   y = 3x + 0.5
   y = 3x

These lines are ALL parallel.
They all have the same slope (m).
(Remember y = mx + b.)

 

Example:
The slope of
is and .  Find the slope of .
Since the lines are parallel, the slopes are the same.
The slope of is also
ANSWER

 

 

Perpendicular Lines:
                          (negative reciprocal slopes!)

 

Perpendicular lines have negative reciprocal slopes.

The symbol to indicate perpendicular is an up-side-down capital T.

where l1 and l2 are lines
m1 and m2 are slopes

 

To find a negative reciprocal of a number, flip the number over (invert) and negate that value. 

 

  

These lines are perpendicular.
Their slopes (m) are negative reciprocals.
(Remember y = mx + b.)

 

Example:
The slope of
is and .  Find the slope of .
Since the lines are perpendicular, the slopes are negative reciprocals.
The slope of is
ANSWER