Results 1 to 3 of 3

Math Help - Equation of the line perpendicular to.....

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    9

    Equation of the line perpendicular to.....

    Hi

    I am back studying after a few years away from it and I wonder if someone will be able to give a bit of advice.
    The question i am needing help with is this-
    Determine the equation of the line perpendicular to 4x+3Y+5=0 passing through the point (2,4).
    The notes I have been given for the Maths class are very poor and was wondering if someone could help or maybe send me a link to a good tutorial website.

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,400
    Thanks
    1849
    Quote Originally Posted by Beginner View Post
    Hi

    I am back studying after a few years away from it and I wonder if someone will be able to give a bit of advice.
    The question i am needing help with is this-
    Determine the equation of the line perpendicular to 4x+3Y+5=0 passing through the point (2,4).
    The notes I have been given for the Maths class are very poor and was wondering if someone could help or maybe send me a link to a good tutorial website.

    Thanks
    Any (non-vertical) line can be written in the "slope-intercept" form y= mx+ b where m is the "slope" and b is the "y-intercept". Write your given line in that form to find its slope. A line perpendicular to y= mx+ b has slope -1/m. You can use the fact that it passes through (2, 4) to find b.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member teuthid's Avatar
    Joined
    Feb 2008
    From
    Bowling Green, OH
    Posts
    49
    In order to write the equation for a line we need two pieces of information:
    (1) A point on the line
    (2) The slope of the line

    This problem gives us a point for free: (2,4). Unfortunately we're going to have to work to find the slope. We know that our line is going to be perpendicular to their line (4x+3y+5=0), so if we can find the slope of their line we'll know what ours should be (I'll explain how in a little bit).

    Finding the Slope of their line:
    ======================
    To find the slope of a line from its equation just solve for y, and whatever the x coefficient turns out to be, that is the slope...

    \begin{array}{lrcl}<br />
&4x+3y+5 &=& 0\\<br />
\Rightarrow& 4x+3y &=&-5\\<br />
\Rightarrow& 3y&=&-4x-5\\<br />
\Rightarrow& y &=& -\frac{4}{3}x-\frac{5}{3}<br />
\end{array}

    So the slope of their line is -\frac{4}{3}

    Find the Slope of our line:
    ===================
    If they had asked us to find a parallel line, we would have our slope already--we'd just use the slope of their line. However, since we're looking for a perpendicular line, we have to make two adjustments to their slope to get ours:
    (1) change the sign
    (2) take the reciprocal

    Changing the sign and taking the reciprocal of -\frac{4}{3} gives us \frac{3}{4}.

    Writing the equation:
    ================
    When you've got a point (let's call it (x_0,y_0)) and a slope (let's call it m), the easiest equation to write is point-slope form:

    y-y_0=m(x-x_0)

    For us, (x_0,y_0) is (2,4) and m is \frac{3}{4}, so just plug the appropriate values in and you'll have your equation!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: May 12th 2011, 01:18 PM
  2. Perpendicular Line/Equation
    Posted in the Geometry Forum
    Replies: 2
    Last Post: June 5th 2009, 07:46 AM
  3. Replies: 11
    Last Post: June 2nd 2009, 07:08 PM
  4. Replies: 1
    Last Post: October 23rd 2008, 04:39 AM
  5. equation of a line perpendicular to the line defined
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: June 6th 2007, 10:02 AM

Search Tags


/mathhelpforum @mathhelpforum