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Math Help - Straight line equation

  1. #1
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    Straight line equation

    What is the equation of the line that intersects line y = mx + b
    at point (1, m+b)?
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  2. #2
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    "The" line?
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  3. #3
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    Quote Originally Posted by Wilmer View Post
    What is the equation of the line that intersects line y = mx + b
    at point (1, m+b)?


    This question makes no sense: at any point in the (real euclidean) plane there infinite lines that contain that point.

    Tonio
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  4. #4
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    Ok (quite simple); was looking for y = bx + m as the unique answer:
    lines y = mx + b and y = bx + m intersect at (1, m+b);
    how should I word the question ? Thanks.
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  5. #5
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    Quote Originally Posted by Wilmer View Post
    Ok (quite simple); was looking for y = bx + m as the unique answer:
    lines y = mx + b and y = bx + m intersect at (1, m+b);
    how should I word the question ? Thanks.


    Well, perhaps: what's the line that passes through (1,m+b) and has a slope equal to m?

    Tonio
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  6. #6
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    Thanks you guys who answered; this I guess requires a li'l more explaining.
    To start, I would have rather posted this in "puzzle" section, but was told
    to post it here by a moderator; again, probably because I wasn't clear!

    During the hockey game Monday night when Boston demolished Vancouver 8=1,
    I was (during commercials...) playing around with graph paper : straight lines.

    I graphed line y = 5x + 3 (m=5, b=3) ; some points on it: (0,3), *(1,8), (2,13) ....

    Bored, I decided to see what happens if I switch m and b, thus y = bx + m,
    so y = 3x + 5 (m=3, b=5); some points on it: (0,5), *(1,8), (2,11) ....

    Now I noticed that the 2 lines intersect at point *(1,8) : or at (1, b+m).

    I graphed a few other cases: intersection always (1, b+m).

    Of course, from the 2 equations we have equality mx + b = bx + m,
    which leads to x = 1 ; then to y = m + b.

    So, without further ado, I put up my question...
    SORRY for not being clearer

    Btw, any suggestions as to how to "word" this differently will be appreciated.

    Like:
    Line#1 (y = mx + b) and Line#2 intersect at point (1, b+m).
    Using same variables (x,y,m,b), what is Line#2's equation?

    Looks like I need to get a life !!
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