parallel and perpendicular lines in the cartesian plane
DESCRIPTION
Parallel and Perpendicular Lines in the Cartesian Plane. Stereotypes about Parallel and Perpendicular Lines. They are boring! They have no use in life . Just a series of lines with positive slopes… No Big Deal. Color coded to show parallel and perpendicular lines. WHOA!. - PowerPoint PPT PresentationTRANSCRIPT
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Parallel and Perpendicular Lines in the
Cartesian Plane
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They are boring!
They have no use in life.
STEREOTYPES ABOUT PARALLEL AND PERPENDICULAR LINES
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Just a series of lines with positive slopes…
No Big Deal
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Color coded to show
parallel and
perpendicular lines
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WHOA!
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I know… I’m Awesome!
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PARALLEL AND PERPENDICULAR LINES ARE EVERYWHERE
Construction
Maps
Sports
Artwork
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y = mx + b m is the slope of the lineb is the y-intercept
REVIEW: SLOPE INTERCEPT FORM
Life is easy when you’re
in slope
intercept form
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y = mx + bThe 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/function-grapher.php
Y -INTERCEPT
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my = mx + bSlope Slider
Slope ofvertical lines?
SLOPE(𝑥1 , 𝑦1)
(𝑥2 , 𝑦 2)
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3y = 6x + 95y = 10xy = -1x = 3
IDENTIFYING THE SLOPE AND THE Y-INTERCEPT
Hint
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y = mx + bGiven the slope, m, and a point, (x , y), then we can find b, the y-intercept.
b = y – mxOnce we find b, we can find the equation of the line.
REVIEW: FINDING THE EQUATION OF THE LINE GIVEN A SLOPE AND A POINT ON THE LINE
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p = (-2 , 2) m = 4
p = (-3 , 4) m = -2
p = (-2 , 2/3) m = -4/3
PRACTICE: FINDING THE EQUATION OF THE LINE GIVEN THE SLOPE AND A POINT ON THE LINE
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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.
GRAPHING ACTIVITY
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PARALLEL LINESTwo lines
are parallel
The lines never
intersect
Slopes are
equal
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y = (1/3)x + 2 y – 1 = 6x2y = 5x + 34y = 8xy = 6x = -3
FIND THE SLOPE OF A PARALLEL LINE
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PERPENDICULAR LINESTwo lines
are perpendicul
ar
The lines intersect at right angle
Slopes are negative reciprocal
s
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y = -3x – 2y = (1/3)x + 2 y – 1 = 6x2y = 5x + 3y = 6x = -3
FIND THE SLOPE OF A PERPENDICULAR LINE
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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 PARALLEL LINE THAT PASSES THROUGH THE GIVEN POINT.
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y = -3x – 2 , p = (-1 , 4)
4y = 8x , p = (1 , 1/3)
y = 6 , p = (6 , 0)
x = -3 , p = (1 , 2)
FIND THE EQUATION OF THE PERPENDICULAR LINE THAT PASSES
THROUGH THE GIVEN POINT.