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Math Help - Linear Supply Functions?

  1. #1
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    Linear Supply Functions?

    I'm trying to find out the linear supply function and this is what I have so far, which may be all wrong.

    (60, 40) and (100, 60)
    M = 60 40/ 100 60 = 20/40
    S (x) 60 = 20/40 (x 60)


    Supply: For a new diet pill, 60 pills will be supplied at a price of $40, while 100 pills will be supplied at a price of $60. Write a linear supply function for this product.
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  2. #2
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    You've got the right idea. You have the points:

    (60, 40) and (100, 60). You want to find the slope, as you know, but you found the slope incorrectly. The slope is the difference in the y-coordinates divided by the difference in the x-coordinates:

    \frac{40-60}{60-100} = \frac{-20}{-40} = \frac {1}{2}.

    So now you know the slope, m. Use point-slope form (with either point) to write the equation. Point-slope form:

    (y - y_1) = m(x-x_1)

    where (x_1,y_1) are the coordinates of EITHER of your two points, your choice.
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  3. #3
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    Thanks so much for your help. I came up with this answer for the linear supply equation so hopefully this is right.
    S (x) = 1
    ----x - 10
    2
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  4. #4
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    Thanks so much for your help. I came up with this answer for the linear supply equation so hopefully this is right.
    S (x) =
    1
    ----x - 10
    2
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  5. #5
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    Not quite what I got - I got y = \frac{1}{2}x+10, not -10.

    (y-40)= \frac{1}{2}(x-60)

    y - 40 = \frac{1}{2}x - 30

    Add 40 to both sides gives:

    y = \frac{1}{2}x+10.

    Perhaps just a sign error, I suspect.
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