Parallel lines postulate postulate 17

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Parallel lines postulatepostulate 17

• If 2 lines are parallel, then they have the same
  slope
• All vertical lines are parallel to each other

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Perpendicular lines postulatepostulate 18

• If 2 nonvertical lines are perpendicular, then
  the product of their slopes is -1.
• Vertical and horizontal lines are perpendicular
  to each other.
• When the product of 2 numbers is -1, they are
  opposite reciprocals,
• So whenever 2 lines have slopes that are opposite
  reciprocals of each other , they are
  perpendicular lines

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What is the slope of a vertical line?

• UNDEFINED
• Undefined slopes cannot be equal to each other
• No product can be found with an undefined slope

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Finding slopes of parallel and perpendicular lines

• Find the slope of a line through the points (1,0)
  and (0,-3)
• Find the slope of a line parallel to it.
• Find the slope of a line perpendicular to it.

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Identifying parallel and perpendicular lines

• Are these lines parallel, perpendicular or
  neither?
• y 2x4 2y 1 4x
• y -3 2x 2y 1-4x
• y 3-1.5x 12-4x 4y 3x
• y -7 1.5 x 7x 4y 8 0

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Point-slope form of a line

• y-y1 m(x-x1)
• Sometimes it is helpful to find a line passing
  through a given point that is parallel or
  perpendicular to another line. Point-slope
  formula can be used to solve these.

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Find a line parallel to y x2 and passes
through the point (3,8)

• Point-slope form slope-intercept form
• y-y1m(x-x1) y mx b
• y-81(x-3) y 1 x b
• y-8x-3 8 1(3) b
• y x5 5 b
• y x 5

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Find a line that is parallel to y -3/2 x 3
and passes through (-4,3)

• Point-slope form slope-intercept form

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Find a line perpendicular to y2/3x and passes
through (2,4)

• Point-slope form slope-intercept form
• Slope of perpendicular line is -3/2
• y-4-3/2(x-2) y -3/2 xb
• y-4 -3/2x 3 4 -3/2(2) b
• y -3/2x 7 4 -3 b
• 7 b
• y -3/2x 7

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