12/23/2015 3-3: slopes of lines 1 expectation: you will calculate slopes of lines parallel and...
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04/21/23 3-3: Slopes of Lines 1
3-3: Slopes of Lines3-3: Slopes of Lines
Expectation:You will calculate slopes of lines parallel and
perpendicular to given lines.
04/21/23 3-3: Slopes of Lines 2
SlopeSlope
x
y
(x1,y1)
(x2,y2)
rise
run
Slope: m= riserun =
y2-y1
x2-x1
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SlopeSlope
x
y
(-4,-4)(-3,-2)
(-1,2)
m=2-(-4)
-1-(-4)=
63
=21
m=-2-(-4)
-3-(-4)=
21
Points used does not matter!!!
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What is the slope of the line What is the slope of the line below?below?
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Calculate the slope of the Calculate the slope of the line through:line through:
(4,7) and (-5, 12)
04/21/23 3.8: Analyzing Polygons
In the standard (x,y) coordinate plane, what is the slope of the line joining the points (3,7) and (4,-8)?
A)-15B)-1C)-1/7
D)21/32
E)15
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Horizontal and Vertical Horizontal and Vertical LinesLines
Draw the vertical line through (4,3) and (4,-6).
Calculate the slope of the line.Is this true for all vertical lines?Draw the horizontal line through (3,5)
and (-3,5).What is the slope of this line?Is this true for all horizontal lines?
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Horizontal and Vertical Horizontal and Vertical Lines Slopes Theorem:Lines Slopes Theorem:
The slope of all vertical lines is ____________.
The slope of all horizontal lines is ___________.
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Slopes and LinesSlopes and LinesPositive slope: line goes _____ from left
to rightNegative slope: line goes ______ from
left to rightUndefined slope: ____________ lineSlope of zero: _____________ line
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Parallel Lines and SlopesParallel Lines and SlopesGraph -3x + y = 4 and -3x + y = 1 on
the same grid.What appears to be true about the
lines?Calculate the slope of each line.Make a conjecture about the slopes of
parallel lines.
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Parallel Lines and Slopes Theorem:Two nonvertical lines are parallel iff their slopes are _______________.
All vertical lines are ____________.
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Perpendicular Lines and Perpendicular Lines and SlopesSlopes
Carefully graph y = -2.5x – 2 and y = .4x + 4 on the same grid.
Measure the angle formed by the lines.What appears to be true about the
lines?Calculate the slopes of the lines.Make a conjecture about the slopes of
perpendicular lines.
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Perpendicular Lines and Perpendicular Lines and Slopes Slopes
TheoremTheorem
Two nonvertical lines are perpendicular iff the product of their slopes is ____. Horizontal and vertical lines are ___________________.
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Determine whether the followinglines are parallel, perpendicular or neither:
-2x + y = 4.5x + y = 8
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Calculate x so that the line through the points has slope of
5
2
A(x,10) B(5,15)
What is the slope of a line that is parallel to the line determined by the equation
5x – 4y = 8? A)-4B)-5/4
C)5/4
D)2E)4
04/21/23 3-3: Slopes of Lines 20
What is the slope of a line perpendicular to the line determined by the equation 7x + 4y = 11?
A)-4B)-7/4
C)11/4
D)4E)4/7
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Assignment:Assignment:
pages 142-143,pages 142-143,#17, 23, 27, 29, 39-43 (odds), 49#17, 23, 27, 29, 39-43 (odds), 49