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  1. #1
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    showing

    Show that the intersection point of y=-x+1 and x=2b lies on the line y=m(x-2b)+(1-2b)
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  2. #2
    Senior Member BAdhi's Avatar
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    Re: showing

    what is your progress so far?
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  3. #3
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    Re: showing

    What, exactly, is the intersection point of y= -x+ 1 and x= 2b? Does it satisfy the equation y= m(x- 2b)+ (1- 2b)? And is that "for some m" or "for all m"?
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  4. #4
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    Re: showing

    Quote Originally Posted by HallsofIvy View Post
    What, exactly, is the intersection point of y= -x+ 1 and x= 2b? Does it satisfy the equation y= m(x- 2b)+ (1- 2b)? And is that "for some m" or "for all m"?
    the exact intersection point is when y=1-2b

    when y=1-2b, for y= m(x- 2b)+ (1- 2b),

    1-2b=m(x- 2b)+ (1- 2b)
    m(x-2b)=0
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  5. #5
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    Re: showing

    Quote Originally Posted by Punch View Post
    the exact intersection point is when y=1-2b

    when y=1-2b, for y= m(x- 2b)+ (1- 2b),

    1-2b=m(x- 2b)+ (1- 2b)
    m(x-2b)=0
    To put it more simply,
    the point of intersection of the lines

    y=1-x and x=2b is (2b,\;1-2b)

    Now to show that this point lies on the other,
    simply insert the co-ordinates to see that equality is maintained.
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