Parallel and Perpendicular Lines in the Cartesian Plane

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STEREOTYPES ABOUT
PARALLEL AND PERPENDICULAR LINES
They are boring!
They have no use in life.
PARALLEL AND PERPENDICULAR LINES
ARE EVERYWHERE
REVIEW: SLOPE INTERCEPT FORM
y = mx + b
m is the slope of the line
b is the y-intercept
Life is easy
when you’re in
slope intercept
form
Y -INTERCEPT
y = mx + b
The y-intercept is the y value when x = 0.
Visually, the y-intercept is y value when the
line crosses the y axis
http://www.mathsisfun.com/data/functiongrapher.php
(2 , 2 )
SLOPE
y = mx + b
Slope Slider
∆
∆
(1 , 1 )
Slope of
vertical lines?
 − 
 − 
m
 − 
 − 
IDENTIFYING THE SLOPE
AND THE Y-INTERCEPT
3y = 6x + 9
5y = 10x
y = -1
x=3
REVIEW:
FINDING THE EQUATION OF THE
LINE GIVEN A SLOPE AND A POINT ON THE LINE
y = mx + b
Given the slope, m, and a point, (x , y),
then we can find b, the y-intercept.
b = y – mx
Once we find b, we can find the equation of the
line.
PRACTICE: FINDING THE EQUATION OF THE LINE
GIVEN THE SLOPE AND A POINT ON THE LINE
p = (-2 , 2)
m = 4
p = (-3 , 4)
m = -2
p = (-2 , 2/3)
m = -4/3
GRAPHING ACTIVITY
1. Graph line segments.
Be sure that each endpoint is an integer
coordinate, such as (1,3) or (-3,0)
Compute and record their slope.
2. Then graph a parallel line to each of the three
line segments. Compute and record the slopes of
the parallel lines. Then delete the parallel lines.
3. Then graph a perpendicular line to each of the
three line segments. Compute and record the
slopes of the perpendicular lines.
PARALLEL LINES
Two lines
are
parallel
Slopes
are
equal
The lines
never
intersec
t
FIND THE SLOPE OF A PARALLEL LINE
y = (1/3)x + 2
y – 1 = 6x
2y = 5x + 3
4y = 8x
y=6
x = -3
PERPENDICULAR LINES
Two lines are
perpendicular
Slopes are
negative
reciprocals
The lines
intersect at
right angle
FIND THE SLOPE OF A
PERPENDICULAR LINE
y = -3x – 2
y = (1/3)x + 2
y – 1 = 6x
2y = 5x + 3
y=6
x = -3
FIND THE EQUATION OF THE PARALLEL LINE
THAT PASSES THROUGH THE GIVEN POINT.
y = (1/3)x + 2 , p = (2 , -3)
2y = 5x + 3 , p = (1/2 , 2/3)
y = 6 , p = (6 , 0)
x = -3 , p = (1 , 2)
FIND THE EQUATION OF THE PERPENDICULAR
LINE THAT PASSES THROUGH THE GIVEN POINT.
y = -3x – 2 , p = (-1 , 4)
4y = 8x , p = (1 , 1/3)
y = 6 , p = (6 , 0)
x = -3 , p = (1 , 2)

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