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Question:


catlover
Student
High School - 10th Grade

What is a conjecture you can make about lines with equal slopes?

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Posted by catlover on Sunday November 1, 2009 at 2:16 PM and tagged with geometry, math.

Answers:


  1. lynn30k Teacher
    High School - 10th Grade

    eNotes Editor

    When the slopes of different lines are equal, it means the lines must be parallel to each other.  They have different y-intercepts, but are orientated in the same direction.They could also be the same line (same slope and same y-intercept), but I doubt this is what your teacher has in mind.

    Sources:
    http://www.regentsprep.org/regents/math/geometry/GCG1/EqL...

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    Posted by lynn30k on Sunday November 1, 2009 at 4:53 PM

  2. neela
    neela Teacher
    Graduate School

    eNotes Editor

    The two lines have equal slopes implies they are equally inclined to any given line of reference. In other words the two lines are parallel or under extreme case they may coincide into one single line.

    Let y=m1x+c1 and

    y= m2x+c2  be two lines with inclinations of slope m1 and m2 to the X axis and making intercepts c1 and c2 respectively with X axis.

    So if m1 = m2 , then the two lines are parallel as long as c1 and c2 are different.

    Further, if m1=m2 and c1=c2, the lines coincide to be a single line.

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    Posted by neela on Sunday November 1, 2009 at 7:41 PM