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Math Help - parallel & perpendicular lines help

  1. #1
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    parallel & perpendicular lines help

    hey everyone, this is my first post...i hope i can find some help here, as i have searched my math book up and down, only to find no answer.

    i am in college algebra, and the section is parallel & perpendicular lines.

    the problem i am totally stuck on is this...

    Code:
     
    x - y       x + y
    -----  =   -----   - 1
      3            2
     
    AND
     
    7 = - ( x - y ) + 4y
    They want me to rewrite both in slope-intercept form, then find out if they are parallel or perpendicular.


    I would really and truly appreciate any and all help with this...i just don't know what to do

    thanks so much,

    ryan
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by shipwreck View Post
    hey everyone, this is my first post...i hope i can find some help here, as i have searched my math book up and down, only to find no answer.

    i am in college algebra, and the section is parallel & perpendicular lines.

    the problem i am totally stuck on is this...

    Code:
     
    x - y       x + y
    -----  =   -----   - 1
      3            2
     
    AND
     
    7 = - ( x - y ) + 4y
    They want me to rewrite both in slope-intercept form, then find out if they are parallel or perpendicular.


    I would really and truly appreciate any and all help with this...i just don't know what to do

    thanks so much,

    ryan
    Hello Ryan,

    \frac{x-y}{3}=\frac{x+y}{2}-1

    First, let's multiply everything by the LCD of 6 to get rid of those pesky denominators.

    6\left(\frac{x-y}{3}\right)=6\left(\frac{x+y}{2}\right)-6(1)

    2x-2y=3x+3y-6

    Simplify to

    -5y=x-6

    \boxed{y=\frac{-1}{5}x+\frac{6}{5}}

    Now for the other one...

    7=-(x-y)+4y

    7=-x+y+4y

    Simplifying....

    5y=x+7

    \boxed{y=\frac{1}{5}x+\frac{7}{5}}

    Compare the slopes of the two boxed equations. What do you think?
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  3. #3
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    well i know that if both slopes are identical, than they are considered parallel....but these aren't identical, although i don't know if there is a particular rule or not about them being opposites, but NOT being reciprocal negative opposites...

    1/5 x & 1/5x would be parallel, but i am just not 100% certain about 1/5x & -1/5x. i would say they are not parallel...right?
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  4. #4
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    anyone able to confirm if i am right or not about these being parallel or not?
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  5. #5
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by shipwreck View Post
    anyone able to confirm if i am right or not about these being parallel or not?
    You answered your question yourself. If the slopes are not the same then they aren't the parallel
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