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Math Help - Parametric equations 2

  1. #1
    Junior Member
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    Parametric equations 2

    I have to select the best description for the curve given by the parametric equation x=t+5, y=2t-1, t in R.

    possible answers are:
    1) a straight line with slope 2.
    2) a straight line through the point (5,1).
    3) a parabola with vertex (-5,1).
    4) a circle centered at (5,-1).
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  2. #2
    MHF Contributor
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    Quote Originally Posted by mike1 View Post
    I have to select the best description for the curve given by the parametric equation x=t+5, y=2t-1, t in R.

    possible answers are:
    1) a straight line with slope 2.
    2) a straight line through the point (5,1).
    3) a parabola with vertex (-5,1).
    4) a circle centered at (5,-1).
    When you see a parameter, try to eliminate the parameter. The parameter here is t. So get rid of t.

    x = t +5
    So, t = x -5 ----------**

    y = 2t -1
    So,
    y = 2(x-5) -1
    y = 2x -10 -1
    y = 2x -11 --------the equationm where the parameter t was eliminated.

    That is a linear equation, a straight line in graph. Its slope is 2, because of the "2x" term.
    [y = mx +b, you know.]

    Therefore, 1) a straight line with slope 2. --------------answer.

    ----------------------------
    Check "2) a straight line through the point (5,1)."
    1 =? 2(5) -11
    1 =? 10 -11
    1 =? -1
    No, so Option (2) is not coorect. Therefore, option (1) is really correct.
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