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The slide show review slope intercept form and provides instruction for a constructivist activity for students to discover the relationship between the slopes of two parallel or two perpendicular lines.
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Parallel and Perpendicular Lines in the
Cartesian Plane
They are boring!
They have no use in life.
STEREOTYPES ABOUT PARALLEL AND PERPENDICULAR LINES
Just a series of lines with positive slopes…
No Big Deal
Color coded to show
parallel and
perpendicular lines
WHOA!
I know… I’m Awesome!
PARALLEL AND PERPENDICULAR LINES ARE EVERYWHERE
Construction
Maps
Sports
Artwork
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
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/function-grapher.php
Y -INTERCEPT
m
y = mx + bSlope Slider
Slope ofvertical lines?
SLOPE
(𝑥1 , 𝑦1)
(𝑥2 , 𝑦 2)
3y = 6x + 9
5y = 10x
y = -1
x = 3
IDENTIFYING THE SLOPE AND THE Y-INTERCEPT
Hint
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
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
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
PARALLEL LINES
Two lines are parallel
The lines never
intersect
Slopes are equal
y = (1/3)x + 2
y – 1 = 6x
2y = 5x + 3
4y = 8x
y = 6
x = -3
FIND THE SLOPE OF A PARALLEL LINE
PERPENDICULAR LINES
Two lines are perpendicular
The lines intersect at right angle
Slopes are negative
reciprocals
y = -3x – 2
y = (1/3)x + 2
y – 1 = 6x
2y = 5x + 3
y = 6
x = -3
FIND THE SLOPE OF A PERPENDICULAR LINE
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.
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.
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