3.6 Parallel Lines in a Coordinate Plane

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3.6 Parallel Lines in a Coordinate Plane

• Geometry
• Mrs. Spitz
• Fall 2005

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Standard/Objectives

• Standard 3 Students will learn and apply
  geometric concepts.
• Objectives
• Find slopes of lines and use slope to identify
  parallel lines in a coordinate plane.
• Write equations of parallel lines in a coordinate
  plane.

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Assignment

• Pgs. 168-170 4-22 24-44

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Slope of parallel lines

• In algebra, you learned that the slope of a
  nonvertical line is the ratio of the vertical
  change (rise) to the horizontal change (run).
• If the line passes through the points (x1, y1)
  and (x2, y2), then the slope is given by
• slope rise
• run
• m y2 y1
• x2 x1

Slope is usually represented by the variable m.
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Ex. 1 Finding the slope of train tracks

• COG RAILWAY. A cog railway goes up the side of
  Mount Washington, the tallest mountain in New
  England. At the steepest section, the train goes
  up about 4 feet for each 10 feet it goes forward.
  What is the slope of this section?
• slope rise 4 feet .4
• run 10 feet

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Ex. 2 Finding Slope of a line

• Find the slope of the line that passes throug the
  points (0,6) and (5, 2).
• m y2 y1
• x2 x1
• 2 6
• 5 0
• - 4
• 5

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Postulate 17 Slopes of Parallel Lines

• In a coordinate plane, two non-vertical lines are
  parallel if and only if they have the same slope.
  Any two vertical lines are parallel.

Lines k1 and k2 have the same slope.
k1
k2
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Ex. 3 Deciding whether lines are parallel

• Find the slope of each line. Is j1j2?

M1 4 2 2 M2 2 2 1
Because the lines have the same slope, j1j2.
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Ex. 4 Identifying Parallel Lines

• M1 0-6 -6 -3
• 2-0 2
• M2 1-6 -5 -5
• 0-(-2) 02 2
• M3 0-5 -5 -5
• -4-(-6) -46 2

k2
k3
k1
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Solution

• Compare the slopes. Because k2 and k3 have the
  same slope, they are parallel. Line k1 has a
  different slope, so it is not parallel to either
  of the other lines.

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Writing Equations of parallel lines

• In algebra, you learned that you can use the
  slope m of a non-vertical line to write an
  equation of the line in slope-intercept form.
• slope y-intercept
• y mx b
• The y-intercept is the y-coordinate of the point
  where the line crosses the y-axis.

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Ex. 5 Writing an Equation of a Line

• Write an equation of the line through the point
  (2, 3) that has a slope of 5.
• y mx b
• 3 5(2) b
• 3 10 b
• -7 b

• Steps/Reasons why
• Slope-Intercept form
• Substitute 2 for x, 3 for y and 5 for m
• Simplify
• Subtract.

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Write the equation

• Because m - 1/3 and b 3, an equation of n2
  is y -1/3x 3

This assignment is due next time we meet.