Results 1 to 3 of 3

Math Help - Help me!

  1. #1
    Member helloying's Avatar
    Joined
    Jul 2008
    Posts
    177

    Help me!

    Given that the x-intercept of a line is twice the y-intercept of its y-intercept and that the line passes thru the intersection between the lines 3y+x=3 and 4y-3x=5, find the eqn of the line. i found the intersection of the line and use the point to find the gradient of the the two point at the x-intercept and x-intercept so that i can eqate them and find the intercept. however i got a large fraction and is very confusing. Did i do wrongly? or is there another method to solve this?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by helloying View Post
    Given that the x-intercept of a line is twice the y-intercept of its y-intercept and that the line passes thru the intersection between the lines 3y+x=3 and 4y-3x=5, find the eqn of the line. i found the intersection of the line and use the point to find the gradient of the the two point at the x-intercept and x-intercept so that i can eqate them and find the intercept. however i got a large fraction and is very confusing. Did i do wrongly? or is there another method to solve this?
    Let the line have equation y = mx + c.

    x-interecept: x = - \frac{c}{m} \Rightarrow 2c = - \frac{c}{m} \Rightarrow m = - \frac{1}{2}.

    Substitute the known point on the line to find c.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,907
    Thanks
    766
    Hello, helloying!

    Given that the x-intercept of a line is twice the y-intercept,
    . . and that the line passes thru the intersection of the lines \begin{array}{c}3y+x\:=\:3 \\ 4y-3x\:=\:5\end{array}
    find the equation of the line.

    The lines intersect at: . P\left(\frac{3}{13},\;\frac{14}{13}\right)


    The line has y-intercept Q(0,\,b) and x-intercept R(2b,\,0)

    The slope of line QR is: . m \:=\:\frac{0-b}{2b-0} \:=\:-\frac{1}{2}


    The line thorugh P\left(\frac{3}{13},\:\frac{14}{13}\right) with slope -\frac{1}{2} has the equation:

    . . y - \frac{14}{13} \:=\:-\frac{1}{2}\left(x - \frac{3}{13}\right) \quad\Rightarrow\quad \boxed{\;y \;=\;-\frac{1}{2}x + \frac{31}{16}\;}

    Follow Math Help Forum on Facebook and Google+


/mathhelpforum @mathhelpforum