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.

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SlopeSlope

x

y

(x1,y1)

(x2,y2)

rise

run

Slope: m= riserun =

y2-y1

x2-x1

04/21/23 3-3: Slopes of Lines 3

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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04/21/23 3-3: Slopes of Lines 9

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

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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