Chapter 3.4 Notes: Find and Use Slopes of Lines

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Chapter 3.4 Notes Find and Use Slopes of Lines

• Goal You will find and compare slopes of lines.

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• The slope of a nonvertical line is the ratio of
  vertical change (rise) to horizontal change (run)
  between any two points on the line.
• If a line in the coordinate plane passes through
  points (x1, y1) and (x2, y2) then the slope, m,
  is

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• Slope of Lines in the Coordinate Plane
• Negative Slope falls from left to right
• Positive Slope rises from left to right
• Zero Slope (slope of 0) horizontal line
• Undefined Slope vertical line

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• Ex.1 Find the slopes of line a and line d.
• Ex.2 Use the graph in Ex.1. Find the slope of
  the line.
• a. Line b b. Line c
  

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• Comparing Slopes
• When two lines intersect in a coordinate plane,
  the steeper line has the slope with greater
  absolute value.
• You can also compare slopes to tell whether two
  lines are parallel or perpendicular.
• Postulate 17 Slopes of Parallel Lines
• In a coordinate plane, two nonvertical lines are
  parallel if and only if they have the same slope.
  
• Any two vertical lines are parallel.

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• Postulate 18 Slopes of Perpendicular Lines
• In a coordinate plane, two nonvertical lines are
  perpendicular if and only if the slopes of the
  two lines are the opposite reciprocals of each
  other.
• Horizontal lines are perpendicular to vertical
  lines.

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• Ex.3 Find the slope of each line. Which lines
  are parallel?
• Ex.4 Line m passes through (-1, 3) and (4, 1).
  Line t passes through (-2, -1) and (3, -3). Are
  the two lines parallel? Explain how you know.

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• Ex.5 Line h passes through (3, 0) and (7, 6).
  Graph the line perpendicular to h that passes
  through the point (2, 5).
• Ex.6 Line k passes through (0, 3) and (5, 2).
  Graph the line perpendicular to k that passes
  through the point (1, 2).
• Ex.7 Line n passes through (0, 2) and (6, 5).
  Line m passes through (2, 4) and (4, 0). Is
  ? Explain.

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• Ex.8 Line q passes through the points (0, 0) and
  
• (-4, 5). Line t passes through the points (0, 0)
  and
• (-10, 7). Which line is steeper, q or t?
• Graph the line through the given point with the
  given slope.
• Ex.9 A(-5, -2) m 4
• Ex.10 A( -2, 3)