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Math Help - Parametric Equations

  1. #1
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    Parametric Equations

    x = -4 + 3t
    y = 1 + 2t
    The displayed equations are called
    parametric, and t is called a parameter. How is the slope of a line determined from its parametric equations?

    * I already know I can find the slope by plugging in values for t and plotting the points or using the slope formula...
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  2. #2
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    m = \dfrac{\Delta y}{\Delta x} = \dfrac{y(t_2) - y(t_1)}{x(t^2) - x(t_1)} = \dfrac{(1+2t_2)-(1+2t_1)}{(-4+3t_2)-(-4+3t_1)} = \dfrac{2(t_2-t_1)}{3(t_2-t_1)} = \dfrac{2}{3}

    in short, note that slope of the line is equal to the rate of change of y divided by the rate of change of x
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