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Math Help - Find the equation of a parallel line

  1. #1
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    Find the equation of a parallel line

    Find the equation of a line which is parallel to the line mx + ny + c = 0 and passing through the point (2,3).


    The given answer is: m(x-2)+n(y-3) = 0, but how do I get there?
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    MHF Contributor red_dog's Avatar
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    The slope of the line mx+ny+c=0 is -\frac{m}{n}

    The equation of the line is

    y-3=-\frac{m}{n}(x-2)\Rightarrow m(x-2)+n(y-3)=0
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by fcabanski View Post
    Find the equation of a line which is parallel to the line mx + ny + c = 0 and passing through the point (2,3).


    The given answer is: m(x-2)+n(y-3) = 0, but how do I get there?
    The lines mx+ny+c=0 for fixed n and m form a series of parallels as c varies.

    So the line you seek is found by finding the value of c so that mx+ny+c=0 goes through (2,3). That is:

    2m+3n+c=0

    or:

    c=-(2m+3n)

    CB
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    Why are the x and y values subtracted from x and y in red dog's answer?
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    MHF Contributor red_dog's Avatar
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    Quote Originally Posted by fcabanski View Post
    Why are the x and y values subtracted from x and y in red dog's answer?
    The equation of a line passing through the point M_0(x_0,y_0) and having the slope m is

    y-y_0=m(x-x_0)
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  6. #6
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    Quote Originally Posted by fcabanski View Post
    Find the equation of a line which is parallel to the line mx + ny + c = 0 and passing through the point (2,3).
    Any line parallel to Mx+Ny+C=0 has the same form Mx+Ny+D=0.
    If it contains the point (2,3) this must be true:
    2M+3N+D=0 or D=-(2M+3N)
    Mx+Ny-(2M+3N)=0
    M(x-2)+N(y-3)=0
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  7. #7
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    Thanks everyone!
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