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Math Help - shade region

  1. #1
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    shade region

    hi,
    i need to shade these regions on a graph:
    shade region-question2.jpg

    i can do the first one and last one as you can see here: but i can't do the other one.

    shade region-here.jpg

    i think the second one would be on 0 but im not sure how to plot it on the graph so can someone help me do this please??


    thanks!
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  2. #2
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    For y<x, you should first draw the line y=x
    and "yes", it goes through the origin
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  3. #3
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    Quote Originally Posted by Archie Meade View Post
    For y<x, you should first draw the line y=x
    and "yes", it goes through the origin
    Using a dotted line instead of a solid line...
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  4. #4
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    what do you mean? draw line for x=y? how would i know this?

    p.s. won't be able to respond for about 40mins! sorry.
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  5. #5
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    The inequality \displaystyle y<x means "all the points for which the \displaystyle y value is less than the \displaystyle x value.

    The easiest way to determine these points (which together form a half-plane) is to find the points where \displaystyle y = x, in other words, to draw the line \displaystyle y = x. Of course, since your inequality uses \displaystyle < and not \displaystyle \leq, that means you can't include those points, which is why you use a dotted line.

    Once you have this line, you shade everything that is not in the required region, i.e. everything above the line (since you want all the points that are below it, i.e. where all the \displaystyle y values are less than the \displaystyle x values).

    Hope that helped...
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  6. #6
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    would this be correct??

    shade region-here.jpg
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  7. #7
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    Yes, you've got the line y=x.
    Remember your other inequalities are < or >,
    so the lines themselves are not part of the inequalities in all 3 cases.

    y<x below that dotted line.

    The point (3,2) is in that region. 2<3
    The point (1,0) is in the region. 0<1
    and so on.
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