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Math Help - Co-ordinate geometry help

  1. #1
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    Co-ordinate geometry help

    Hi, what is the best way to find the equation of a straight line when given to points on the line. ie (x1,y1) and (x2,y2)

    I have been finding the gradient m=y2-y1/x2-x1 and then putting into the formula y-y1 =m(x-x1) but i am doing something wrong as i keep getting different answers to my textbook. Could somebody please solve one for me so i can see how it's done?

    Heres one in my book Find the equation of the line AB when A(-2,4) B(5,3)

    Thanks, Chris.
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  2. #2
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    Find m

    m=\frac{3-4}{5+2}=-\frac17

    Now select one point and apply the point-slope formula.
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  3. #3
    MHF Contributor red_dog's Avatar
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    The equation of a line passing through two points M_1(x_1,y_1), \ M_2(x_2,y_2) is

    \displaystyle\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}

    or \displaystyle\begin{vmatrix}x & y & 1\\x_1 & y_1 & 1\\x_2 & y_2 & 1\end{vmatrix}=0
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  4. #4
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    Hi thanks. Yes i know the formula, it's just i am having trouble using it i am going wrong somewhere with it.
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Chris85 View Post
    Hi thanks. Yes i know the formula, it's just i am having trouble using it i am going wrong somewhere with it.
    Why don't you post your solution and we'll take a look at it.

    -Dan
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  6. #6
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    OK

    A=(-2,4) B=(5,3)

    M= y2-y1/x2-x1 = 3-4/5-(-2) = -1/7

    y-y1/y2-y1 = x-x1/x2-x1

    therefore y-4/3-4 = x-(-2)/5-(-2)

    Am i right so far if so what do i do next?? apologies if it's hard to understand im new and still trying to do the latex
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  7. #7
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    Quote Originally Posted by Chris85 View Post
    OK

    A=(-2,4) B=(5,3)

    M= y2-y1/x2-x1 = 3-4/5-(-2) = -1/7

    y-y1/y2-y1 = x-x1/x2-x1

    therefore y-4/3-4 = x-(-2)/5-(-2)

    Am i right so far if so what do i do next?? apologies if it's hard to understand im new and still trying to do the latex
    Hello,

    you calculated the slope of the line correctly.

    Now you plug in the coordinates of one point into the equation of the line:

    point-slope-formula, see Krizalid's post.
    \frac{y-y_1}{x-x_1} = m~\implies~\frac{y-3}{x-5}=-\frac17 Solve for y:

    y-3 = -\frac17 \cdot(x-5) expand the bracket and solve for y:

    y = -\frac17 \cdot x + \frac{26}7
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  8. #8
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    ok, the answer in my textbook is x+7y-26=0??
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  9. #9
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    Quote Originally Posted by Chris85 View Post
    ok, the answer in my textbook is x+7y-26=0??
    Hi,

    take the result I gave you, multiply both sides by 7 and collect all terms on the LHS - then you'll get the answer which is in your book.
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