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Math Help - Coordinate geometry--

  1. #1
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    Exclamation Coordinate geometry--

    Find the equation of the line through the point (5,2) and parallel to the line 2y-3x=4. Find the value of a if the line ax-(a+1)y+2=0 does not intersect the pair of parallel lines.

    The underlined part is what i could not get.
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  2. #2
    Super Member bigwave's Avatar
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    Cool rewrite

    Quote Originally Posted by Ilsa View Post
    Find the equation of the line through the point (5,2) and parallel to the line 2y-3x=4. Find the value of a if the line ax-(a+1)y+2=0 does not intersect the pair of parallel lines.

    The underlined part is what i could not get.
    well this is a try at it...rewrite
    2y-3x=4 as y=\frac{3}{2}x+2
    Then at (5,2) the eq is y=\frac{3}{2}x-\frac{11}{2}
    Last edited by bigwave; October 21st 2010 at 12:43 PM.
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  3. #3
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    correction

    Quote Originally Posted by Ilsa View Post
    Find the equation of the line through the point (5,2) and parallel to the line 2y-3x=4. Find the value of a if the line ax-(a+1)y+2=0 does not intersect the pair of parallel lines.

    The underlined part is what i could not get.
    1. The pair of parallel lines have the common slope m = \frac32.

    2. ax-(a+1)y+2=0~\implies~y=\dfrac{a}{a+1} \cdot x + \dfrac2{a+1}

    3. If the line in question doesn't intersect the two parallels it must be parallel to both, that means it's slope must be m = \frac32 too. Therefore:

    \dfrac{a}{a+1}=\dfrac32~\implies~2a=3a+3~\implies~  a=-3

    EDIT: @ArchieMeade: Thanks!
    Last edited by earboth; October 20th 2010 at 11:22 PM.
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  4. #4
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    The slopes of all 3 lines must be equal.

    Hence a=-3
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