Results 1 to 4 of 4

Math Help - find possible slopes of line passing thru (4,3) so portion of line in first quadrant

  1. #1
    Member sluggerbroth's Avatar
    Joined
    Apr 2012
    From
    Chicago
    Posts
    108

    find possible slopes of line passing thru (4,3) so portion of line in first quadrant

    ...forms triangle of area 27 wit positive coordinate axes.

    book has answer -3/2 or -3/8

    i found first answeer but not second???
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,695
    Thanks
    450

    Re: find possible slopes of line passing thru (4,3) so portion of line in first quadr

    Quote Originally Posted by sluggerbroth View Post
    ...forms triangle of area 27 wit positive coordinate axes.

    book has answer -3/2 or -3/8

    i found first answeer but not second???
    let x_i and y_i represent the positive x and y intercepts of the line

    \frac{x_i \cdot y_i}{2} = 27 \implies x_i \cdot y_i = 54

    slope of the line is m = -\frac{y_i}{x_i}

    y = mx + b

    3 = -\frac{y_i}{x_i} \cdot 4 + y_i

    3 = -y_i\left(\frac{4}{x_i} -1\right)

    3 = -\frac{54}{x_i} \left(\frac{4}{x_i} -1\right)

    3 = -\frac{216}{x_i^2} + \frac{54}{x_i}

    3x_i^2 = -216 + 54x_i

    3x_i^2 - 54x_i + 216 = 0

    x_i^2 - 18x_i + 72 = 0

    (x_i - 6)(x_i - 12) = 0

    x_i = 6 \implies y_i = 9 ... m = -\frac{9}{6} = -\frac{3}{2}

    x_i = 12 \implies y_i = 4.5 ... m = -\frac{4.5}{12} = -\frac{9}{24} = -\frac{3}{8}


    also, in future please post entire problem within the post ... not part in the title, rest in the post. thanks.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member sluggerbroth's Avatar
    Joined
    Apr 2012
    From
    Chicago
    Posts
    108

    Re: find possible slopes of line passing thru (4,3) so portion of line in first quadr

    how do know negative slope? ie m=-y/x??
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,695
    Thanks
    450

    Re: find possible slopes of line passing thru (4,3) so portion of line in first quadr

    Quote Originally Posted by sluggerbroth View Post
    how do know negative slope? ie m=-y/x??
    ...forms triangle of area 27 wit positive coordinate axes
    I always make a sketch before working on a problem ... I'm sure that you do, also, right?
    Attached Thumbnails Attached Thumbnails find possible slopes of line passing thru (4,3) so portion of line in first quadrant-triangle.jpg  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: March 9th 2011, 08:09 PM
  2. line passing through
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 30th 2010, 01:46 AM
  3. Replies: 3
    Last Post: March 17th 2010, 02:22 AM
  4. Replies: 2
    Last Post: September 6th 2009, 09:24 AM
  5. Line passing through a square
    Posted in the Geometry Forum
    Replies: 5
    Last Post: August 26th 2008, 03:29 AM

Search Tags


/mathhelpforum @mathhelpforum