Aim: What is the relationship between slopes of parallel lines?
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Transcript of Aim: What is the relationship between slopes of parallel lines?
Aim: Slopes of Parallel Lines Course: Applied Geometry
Do Now:
a. y = 2x + 5
b. y = 2x – 1
c. y = 2x + 2
Aim: What is the relationship between slopes of parallel lines?
What is the slope of each line?
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Aim: Slopes of Parallel Lines Course: Applied Geometry
Slopes of Parallel Lines
Graph Equations a), b), and d) on the graphing calculator by
1. Clicking the Y = button and inputting
Y1 = 2x + 5
Y2 = 2x – 1
Y3 = 2x + 2
2. Click the Graph key and watch the graphs appear. Hit the Trace key and skip from line to line. Lines having equal slopes are parallel.
Lines having different slopes are not parallel.
Aim: Slopes of Parallel Lines Course: Applied Geometry
Points A(-4, 2), B (1, 2), C(1, -3) and D(-4, -3) form a quadrilateral.
a. Graph the points and draw quadrilateral ABCD
b. What are the slopes of sides AB, BC, CD and AD?
c. What kind of quadrilateral is ABCD? Explain
Model Problem
Aim: Slopes of Parallel Lines Course: Applied Geometry
Model Problem
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B(1, 2)(-4, 2)A
C(1, -3)(-4, -3)D
5 units
5 units4 equal sides
4 right angles
SQUARE
Slope of AB = 0
Slope of CD = 0
Slope of AD = undefined
Slope of BC = undefined
Recall: Two lines are parallel if their slopes are equal and if the slopes of two lines are equal, the lines are parallel. AB || CD & AD || BC
Aim: Slopes of Parallel Lines Course: Applied Geometry
Model Problem
Quadrilateral ABCD has vertices A(0,-1), B(0,1), C(3,4), and D(3,2). Using coordinate geometry, determine what type of quadrilateral ABCD is.
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B
C(3,4)
(0,1)
(0,-1)
(3,2)D
Just showing the graph is not enough - prove using the formula for slope.
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BCslope
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ADslope
UndefinedABslope
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Since the slope of BC and AD are the same, the lines are parallel.
Since the slope of AB and CD are the same, the lines are parallel.
BC || AD, AB || CD, ABCD is a parallelogram.
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yymslope
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Aim: Slopes of Parallel Lines Course: Applied Geometry
Model Problem
Graph a line that is parallel to the line y = 2x – 2 and that has a y-intercept of 4
What is the equation of this new line?
(0, 4)
(1, 6)
(0, -2)
y =
2x -
2
y = 2x + 4
m = 2
m = 2 b = 4
y = mx + b
b = -2
Aim: Slopes of Parallel Lines Course: Applied Geometry
Model Problem
Graph a line that is parallel to the line y = 1/2x – 4 and that passes through point (2, 2)
What is the equation of this new line?
m = 1/2
y = 1/2x – 4
y = 1/2x + 1
y = mx + b
m = 1/2 b = 1
(4, 3)(2, 2)
(0, -4)
b = -4(0, 1)
Aim: Slopes of Parallel Lines Course: Applied Geometry
On Sketchpad:
Graph a line that is parallel to the line y = -1/4x + 3 and that passes through (3, 0).
Sketchpad:
GraphPlot New Function y = -1/4x + 3Enter
GraphPlot Points (3, 0)Plot
Plot a second point that would result in a line parallelto y = -1/4x + 3
Highlight new line Measure Slope and a 2nd timefor Equation.
On your calculator, sent the new equation Y1=
Model Problem
Aim: Slopes of Parallel Lines Course: Applied Geometry
Model Problem
Graph a line that is parallel to the line y = 2x + 1 and that passes through (0, -2).
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Aim: Slopes of Parallel Lines Course: Applied Geometry
Model Problem
Graph a line that is parallel to the line y = -4x – 5 and that passes through (0, 2).
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Aim: Slopes of Parallel Lines Course: Applied Geometry
Model Problem
Graph a line that is parallel to the line y = -4 and that passes through (0, -6).
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Aim: Slopes of Parallel Lines Course: Applied Geometry
Model Problem
Graph a line that is parallel to the line y = 1/3x – 6 and that passes through (1, 2).
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Aim: Slopes of Parallel Lines Course: Applied Geometry
Model Problem
Graph a line that is parallel to the line 2y = 4x – 6 and that passes through (-2, -4).
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