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Math Help - I need help with these 2 problems i just can't figure out for the life of me

  1. #1
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    I need help with these 2 problems i just can't figure out for the life of me

    are these lines perpendicular, parallel, the same, or neither

    (1.) y =2/3 x + 3 and y = -3x + 2

    (2.) 2x + 5y = 1 and y = 5/2x +4
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  2. #2
    MHF Contributor red_dog's Avatar
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    Let d_1:y=m_1x+n_1 and d_2:y=m_2x+n_2.

    d_1\parallel d_2\Leftrightarrow m_1=m_2, \ n_1\neq n_2

    d_1\perp d_2\Leftrightarrow m_1\cdot m_2=-1

    d_1=d_2\Leftrightarrow m_1=m_2, \ n_1=n_2
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  3. #3
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    Hello tyonna!

    Quote Originally Posted by tyonna View Post
    are these lines perpendicular, parallel, the same, or neither

    (1.) y =2/3 x + 3 and y = -3x + 2

    (2.) 2x + 5y = 1 and y = 5/2x +4
    You have to check some criteria


    Let two lines given by

    y1 = ax+b
    y2 = cx+d

    they are perpendicular, if a*c = -1

    they are parallel, if a=c (and b is not equal to d)

    Now back to your excersice

    (1)y =2/3 x + 3 and y = -3x + 2

    It is a = 2/3 and c = -3. It is obvious that these lines are not parallel

    EDIT:
    But it is a*c = 2/3 * (-3) = -2

    This is not equal to -1, because -2 \not= -1

    So they are not perp.


    Number 2
    2x + 5y = 1 and y = 5/2x +4

    Solve the first "line" for y
    2x + 5y = 1

    5y = 1-2x

    y =1/5 * (1-2x) = 1/5 - 2/5x = -2/5x+1/5

    Okay, and the other line is defined by y = 5/2x +4

    It is a = -2/5 and c = +5/2 => they are not parallel, but perpendicular.

    Yours
    Rapha
    Last edited by Rapha; September 18th 2009 at 09:43 PM. Reason: I made a mistake...
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  4. #4
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    Quote Originally Posted by red_dog View Post
    Let d_1:y=m_1x+n_1 and d_2:y=m_2x+n_2.

    d_1\parallel d_2\Leftrightarrow m_1=m_2, \ n_1\neq n_2

    d_1\perp d_2\Leftrightarrow m_1\cdot m_2=-1

    d_1=d_2\Leftrightarrow m_1=m_2, \ n_1=n_2
    what?
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  5. #5
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    Quote Originally Posted by tyonna View Post
    what?
    These are the criteria I mentioned

    Two lines are given by

    Quote Originally Posted by red_dog View Post
    Let d_1:y=m_1x+n_1 and d_2:y=m_2x+n_2.

    They are parallel, if

    Quote Originally Posted by red_dog View Post
    d_1\parallel d_2\Leftrightarrow m_1=m_2, \ n_1\neq n_2

    They are perpendicular/orthogonal, if
    Quote Originally Posted by red_dog View Post
    d_1\perp d_2\Leftrightarrow m_1\cdot m_2=-1
    and they are the same/identical, if
    Quote Originally Posted by red_dog View Post
    d_1=d_2\Leftrightarrow m_1=m_2, \ n_1=n_2
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  6. #6
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    Quote Originally Posted by Rapha View Post
    Hello tyonna!



    You have to check some criteria


    Let two lines given by

    y1 = ax+b
    y2 = cx+d

    they are perpendicular, if a*c = -1

    they are parallel, if a=c (and b is not equal to d)

    Now back to your excersice

    (1)y =2/3 x + 3 and y = -3x + 2

    It is a = 2/3 and c = -3. It is obvious that these lines are not parallel

    But it is a*c = 2/3 * (-3) = -1

    So they are perpendicular.

    Number 2
    2x + 5y = 1 and y = 5/2x +4

    Solve the first "line" for y
    2x + 5y = 1

    5y = 1-2x

    y =1/5 * (1-2x) = 1/5 - 2/5x = -2/5x+1/5

    Okay, and the other line is defined by y = 5/2x +4

    It is a = -2/5 and c = +5/2 => they are not parallel, but perpendicular.

    Yours
    Rapha
    okay, so both are perp....I thought so but I was not sure and when I asked a friend they said I was wrong.
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  7. #7
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    Quote Originally Posted by tyonna View Post
    okay, so both are perp....I thought so but I was not sure and when I asked a friend they said I was wrong.

    Ooooops, Sorry, I'm wrong. I made a mistake.

    In (1) I wrote:

    But it is a*c = 2/3 * (-3) = -1

    a*c = -2, so they are not perp. And not parallel.
    Sorry for that
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  8. #8
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    Quote Originally Posted by Rapha View Post
    Ooooops, Sorry, I'm wrong. I made a mistake.

    In (1) I wrote:

    But it is a*c = 2/3 * (-3) = -1

    a*c = -2, so they are not perp. And not parallel.
    Sorry for that
    So are they neither or the same? Dang, I was happy there for a minute. I thought I could tell my friend, "told you so" glad I hadn't done that yet! Thanks
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  9. #9
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    Quote Originally Posted by tyonna View Post
    So are they neither or the same? Dang, I was happy there for a minute.
    They can't be the same, because a \not= c.

    They are the same, if
    a) the lines are parallel, that means a=c, e. g. m_1 = m_2
    AND
    b) b = d, e. g. in red_dog 's post the criteria is n_1 = n_2

    'Neither' is the right answer for (1)

    Quote Originally Posted by tyonna View Post
    I thought I could tell my friend, "told you so" glad I hadn't done that yet! Thanks
    I'm really sorry for that
    I'm glad you didn't go offline and checked the forum again.
    Last edited by mr fantastic; September 18th 2009 at 11:51 PM. Reason: Added close quote tag.
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  10. #10
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    [QUOTE=Rapha;367561]
    Quote Originally Posted by tyonna View Post
    So are they neither or the same? Dang, I was happy there for a minute.

    They can't be the same, because a \not= c.

    They are the same, if
    a) the lines are parallel, that means a=c, e. g. m_1 = m_2
    AND
    b) b = d, e. g. in red_dog 's post the criteria is n_1 = n_2

    'Neither' is the right answer for (1)



    I'm really sorry for that
    I'm glad you didn't go offline and checked the forum again.
    ok thanks
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