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Math Help - Function notation

  1. #1
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    Function notation

    Find the equation of the line. Write the equation using function notation.
    Through (-2,4); perpendicular to f(x)=-2x+3


    The answer is 1/2x +5 but I dont know how they got that.



    2nd question


    Through (6,-6); parallel to 5x+6y=18


    the answer is -5/6x-1

    I got y=-5/6x-1



    My teacher gave me the cheat sheet for the review to make sure when I study that I can correct them.
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  2. #2
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    Re: Function notation

    If you can please show your work so I can learn from it please! Thank you!
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  3. #3
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    Re: Function notation

    Quote Originally Posted by daword177 View Post
    Find the equation of the line. Write the equation using function notation.
    Through (-2,4); perpendicular to f(x)=-2x+3


    The answer is 1/2x +5 but I dont know how they got that.



    2nd question


    Through (6,-6); parallel to 5x+6y=18


    the answer is -5/6x-1

    I got y=-5/6x-1



    My teacher gave me the cheat sheet for the review to make sure when I study that I can correct them.
    I'll show you how to do the first, you can use that to answer the second.

    The first function is f(x) = -2x + 3, so the gradient of that line is -2.

    The product of the gradients of perpendicular lines is -1, so that means the gradient of the normal must be 1/2 (since 1/2 x -2 = -1).

    So for your normal, so far you have y = (1/2)x + c.

    You are given a point that lies on this normal, namely (x, y) = (-2, 4), so substituting this in gives

    4 = (1/2) x (-2) + c
    4 = -1 + c
    5 = c.

    Therefore the equation of the normal is y = (1/2)x + 5.

    In function notation this is \displaystyle \begin{align*} \mathbf{R} \to \mathbf{R} \left\{ (x, y) | y = \frac{1}{2}x + 5  \right\} \end{align*}


    Now for your second, start by getting your original line in the form y = mx + c.
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    Re: Function notation

    thank you !
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