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Equations of Parallel and Perpendicular Lines

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by Meghan Shinert on 1 February 2014

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Transcript of Equations of Parallel and Perpendicular Lines

Equations of Parallel and Perpendicular Lines
Parallel lines
-lines that lay in the same plane but never meet, no matter how far they extend
When are lines parallel?
Two lines are said to be parallel when they have the same slope.
Review:
The equation of a line is:
y= mx +b

where m= slope and b= y-intercept

to find the slope:
m= (y2-y1)/(x2-x1)
EXAMPLES
1. y= 6x+12 and y= 6x-4
2. y= 7x-2 and y= (1/2)x+4
3. One line passes through the points (0,4) and (1,8). Another line passes through (2,4) and (4,12). Are these lines parallel?
Line 1: m= (8-4)/(1-0)= 4/1= 4

Line 2: m= (12-4)/(4-2)= 8/2= 4

Both have a slope of 4, so yes these lines are parallel.
Perpendicular
Lines

-lines that intersect to form four right angles
When are lines perpendicular?
Two lines are said to be perpendicular when their slopes are negative reciprocals of each other.
Reminder: The reciprocal of any number is found by dividing 1 by that number.

The reciprocal of 2 is 1/2
The reciprocal of 3/2 is 1/(3/2)= 2/3
EXAMPLES
1. y= (-1/2)x+5 and y= 2x-7
2. y= 5x+10 and y= (1/5)x+4
3. One line passes through the points (0,3) and (1,6). Another line passes through (2,-2) and (5,-3). Are these lines perpendicular?
Line 1: m= (6-3)/(1-0)= 3/1=3

Line 2: m= [-3-(-2)]/(5-2)= -1/3
The slope of line 1= 3 and the negative reciprocal of 3 is -1/3, which is the slope of line 2, so yes these lines are perpendicular.
Perpendicular because the
negative reciprocal of 2 is -1/2.
Not perpendicular because 1/5
is the reciprocal of 5, but not the
negative reciprocal.
Parallel because both lines have a slope of 6.
Not parallel because line one has a slope of 7 and line two has a slope of 1/2.
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