1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Graph + Algebra Question

  1. Sep 15, 2007 #1
    1. The problem statement, all variables and given/known data

    Hello, I am a 14 year old boy doing my GCSE's for Maths. And I was doing some past papers and I came across this question which I have never seen before. I looked in textbooks and found none of the sort, and I was wondering if any of you could please help :)

    I have drawn the graph y=x+2/x

    The solutions of the equation 2x+2/x=7 are the x-coordinates of the points of intersection of the graph of y=x+2/x and a straight line L.

    Fine the Equation of L.

    2. Relevant equations


    3. The attempt at a solution

    My guess at the answer would be the equation of the line is y=7 as 2x+2/x=7 means y=2x+2/x=7 as far as I remember. I drew this line on my graph, getting a solution of x=0.3, put this back into the equation and got an answer of 7.23(recurring). Which I thought was close enough allowing for errors, but I really have no idea if it's right or anything, it's just a guess.

    Thanks in advance for any help :)
  2. jcsd
  3. Sep 15, 2007 #2
    Actually, first you need to simplify the equation 2x+2/x=7 to [tex]2x^2-7x+2=0[/tex]. This is a quadratic of the form [tex]ax^2+bx+c=0[/tex] where a=2, b=-7 and c=2.

    The two points you're looking for can be found by [tex]x=\frac{-b+\sqrt{b^2-4ac}}{2a}[/tex] and [tex]x=\frac{-b-\sqrt{b^2-4ac}}{2a}[/tex]

    Next, you plug in the two values you get from here into the equation y=x+2/x to get two values of y.

    Now, you have two points (x1,y1) and (x2,y2) (from your two values of x and y). Using these and the slope intercept form, you can find the equation of the line as such:

    Last edited by a moderator: Sep 15, 2007
  4. Sep 16, 2007 #3

    Thanks alot! Just one question, the last formula you stated, I have never come across it before!! :P Mind explaining it?.. In the meantime, i'll try to figure it out myself, thanks alot though!
  5. Sep 16, 2007 #4


    User Avatar
    Science Advisor

    What eqaution would you use for a straight line through two given points?
  6. Sep 16, 2007 #5
    I'm sorry, I don't know. As far as equations of straight lines goes, i've only ever had to use the basic primary school formula rise/run, which I know is also delta y/delta x. I think I am beginnning to get the solution though, I have plotted the two points on my graph and if I join them I get a straight line. Now when I do this, the gradient of the line is 2.3recurring, which I round off to 2 considering errors, and the Y intercept is about 7. So I think the solution may be y=2x+7.
  7. Sep 16, 2007 #6


    User Avatar
    Homework Helper
    Education Advisor
    Gold Member

    Tigerd12, the straight line L would be some point (x, 7), which when you substitute y=7, would be the line which contains this point. You wrote:
    You are then looking for the solution to a quadratic equation. The solutions will be the x-intercepts, the x coordinates for y=0 (relax; you already made the substitution for y=7 to obtain the equation. You just use algebra to put the equation into the form ax^2 + bx + c =0). Chaoseverlasting gave the right approach.

    You will not really need the equation form for a line given in his message, but you likely need the knowledge as prerequisite development for the kind of question which you are working on; students learning about equations of lines before they learn about quadratic equations.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook