Expectation:

1
3-3 Slopes of Lines

• Expectation
• A3.1.4 Find an equation of the line parallel or
  perpendicular to given line through a given
  point. Understand and use the facts that
  non-vertical parallel lines have equal slopes and
  that non-vertical perpendicular lines have slopes
  that multiply to give -1.

2
Slope
y
run
(x1,y1)
rise
x
(x2,y2)
y2-y1
rise

Slope m
run
x2-x1
3
Slope
y
(-1,2)
x
(-3,-2)
-2-(-4)
(-4,-4)
2
m

1
-3-(-4)
Points used does not matter!!!
4
What is the slope of the line below?
5
Calculate the slope of the line through

• (4,7) and (-5, 12)

6

• In the standard (x,y) coordinate plane, what is
  the slope of the line joining the points (3,7)
  and (4,-8)?
• -15
• -1
• -1/7
• 21/32
• 15

7
Horizontal and Vertical Lines

• 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?

8
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9
Horizontal and Vertical Lines Slopes Theorem

• The slope of all vertical lines is ____________.
• The slope of all horizontal lines is ___________.

10
Slopes and Lines

• Positive slope line goes _____ from left to
  right
• Negative slope line goes ______ from left to
  right
• Undefined slope ____________ line
• Slope of zero _____________ line

11
Parallel Lines and Slopes

• Graph -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.

12
Parallel Lines and Slopes Theorem Two
nonvertical lines are parallel iff their slopes
are _______________. All vertical lines are
____________.
13
Perpendicular Lines and Slopes

• 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 Slopes Theorem
Two nonvertical lines are perpendicular iff the
product of their slopes is ____. Horizontal and
vertical lines are ___________________.
16
Determine whether the following lines are
parallel, perpendicular or neither -2x y
4 .5x y 8
17
Calculate x so that the line through the points
has slope of
A(x,10) B(5,15)
18

• What is the slope of a line that is parallel to
  the line determined by the equation 5x 4y
  8?
• -4
• -5/4
• 5/4
• 2
• 4

19

• What is the slope of a line perpendicular to the
  line determined by the equation 7x 4y 11?
• -4
• -7/4
• 11/4
• 4
• 4/7

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Assignment

• pages 142-143,17, 23, 27, 29, 33-43 (odds), 49