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Math Help - Linear functions

  1. #1
    Ash
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    Linear functions

    What are the steps to solving this problem???

    - Which could be linear functions? Explain.-


    Relation 1:
    x = 1 2 3 3 4
    y= 3 4 5 6 7

    Relation 2:
    x= 5 5 5 5 5
    y= 27 24 21 18 15


    Relation 3:
    x= 0 1 2 3 4
    y= 50 45 40 35 30


    Relation 4:
    x= 3 4 5 6 7
    y= 11 13 17 25 40
    Last edited by Ash; August 29th 2007 at 04:05 PM. Reason: repositioning
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  2. #2
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    Quote Originally Posted by Ash View Post
    What are the steps to solving this problem???

    - Which could be linear functions? Explain.-


    Relation 1:
    x = 1 2 3 3 4
    y= 3 4 5 6 7
    You need to increase (or decrease) by the same amount as you increase x by 1 unit. Do you?
    Relation 2:
    x= 5 5 5 5 5
    y= 27 24 21 18 15
    This is not even a function, why?

    Relation 3:
    x= 0 1 2 3 4
    y= 50 45 40 35 30
    You need to increase (or decrease) by the same amount as you keep increase x by 1 unit. Do you?

    Relation 4:
    x= 3 4 5 6 7
    y= 11 13 17 25 40
    Same idea.
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  3. #3
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    In any function no two ordered pairs have the same second term.
    Why does that rule out the first two?

    In order to be linear the collection of pairs must have a constant relation.
    If \left( {x_1 ,y_1 } \right),\;\left( {x_2 ,y_2 } \right),\;\left( {x_3 ,y_3 } \right) are all pairs in the function then it must be true that
    \frac{{y_1  - y_2 }}{{x_1  - x_2 }} = \frac{{y_3  - y_2 }}{{x_3  - x_2 }} = \frac{{y_1  - y_3 }}{{x_1  - x_3 }}.
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  4. #4
    Ash
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    Thanks for the help. Can you check to see if my conclusions are correct.

    I know relation 1 and 2 are not functions because in both cases the input leads to two or more outputs.

    Relation 3 is a (linear) function because it increases (or decreases) by the same amount- plus, the slope and y-intercept are constant.

    I'm guessing relation 4 is a function but, I gather it's not a (linear) function because, when I calculated the points, the slopes came out to be different.
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  5. #5
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    It seems correct.
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