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Math Help - ax+by=1 form transformations

  1. #1
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    ax+by=1 form transformations

    Hi,

    I'm doing some power studying, so yep, I'm going to be posting a lot of questions. I was just wondering, how do the values of a and b affect the equation ax+by=1? I've Googled some stuff and haven't found any basic list of rules. The only thing I have found (from a practice test and answer key) is that if a>0 and b>0, then the line will have a negative slope and not pass through the 3rd quadrant. Any other rules that I should know about?

    Haha, the Pre-Algebra stuff went right out the window, as you can tell (up until this point in my life I've had Pre-Alg, Alg 1, Geometry, then just finished Alg II this past year). :P

    Thanks!
    imcq
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  2. #2
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    Quote Originally Posted by theimcq View Post
    I was just wondering, how do the values of a and b affect the equation ax+by=1?
    You may find it easier to answer this if you rewrite it in a more common form:

    ax + by = 1

    \Rightarrow by = 1 - ax\Rightarrow y = \frac1b - \frac abx

    The slope-intercept form of an equation of a line is y = mx + b where the slope is m and the y-intercept is (0,\;b). So, looking at our equation, we find that the slope of the line is -\frac ab and the line will intersect the y-axis at \left(0,\;\frac1b\right).

    You can make a few observations from these facts. For example, as \lvert b\rvert increases, the absolute value of the line's slope and y-intercept both decrease and the line becomes flatter and closer to the x-axis.
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  3. #3
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    Thanks so much! I totally forgot about changing it to the mx+b form. Case closed!
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