The point P(4, −2)lies on the curve y = 2/(3 − x).
(a) If Q is the point(x, 2/(3 − x)),use your calculator to find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of x.

1) 3.9 mPQ=
2) 3.99 mPQ=
3)3.999 mPQ=
4) 4.1 mPQ=
5) 4.01 mPQ=

im so confused! i just started this and my teacher really didn't explain it. can someone please break this down for me?

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  1. I will do one of them, you do the others

    3) x = 3.999
    then y = 2/(3-3.999) = -2.00200200200...

    then slope = (-2.002002002 - (-2))/(3.999-4)
    = 2.0020020..

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  2. thank you for answering me. im just trying to figure this out. i understand how the part y= 2/(3-3.999) = -2.002002002

    just your second line im trying to figure out. i can do the others once i just understand the steps. my teacher didn't go over this unfortunately.

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  3. nevermind i understand i took another look at it and its clear. thank you so much for getting back to me!!

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  4. we now had two points
    the original (4,-2) and
    the new (3.999, -2.002002002)

    (notice that these two points are practically on top of each other)

    how do you find the slope between 2 point ?
    if we had 2 points ( a,b) and (c,d) wouldn't it
    be (d-b)/(c-a) or
    you might have been taught
    (y2 - y1)/(x2 - x1)

    that's all I did.

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