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Math Help - Slope of Secant Line

  1. #1
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    Slope of Secant Line

    The slope of the secant line can be written this way:

    f(x + h) - f(x)/h.

    For both questions below, express the slope of the secant line of each function in terms of x and h. Be sure to simplify your answer.

    (1) f(x) = -3x + 2

    (2) f(x) = 1/x

    Also, what exactly is the slope of the secant line?

    What is a secant line anyway?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by symmetry View Post
    The slope of the secant line can be written this way:

    f(x + h) - f(x)/h.


    You need to put the brackets in this properly:

    [f(x + h) - f(x)]/h.

    For both questions below, express the slope of the secant line of each function in terms of x and h. Be sure to simplify your answer.

    (1) f(x) = -3x + 2


    [f(x + h) - f(x)]/h=[(-3(x+h) + 2)-(-3x + 2)]/h=[-3h]/h=-3

    (2) f(x) = 1/x


    [f(x + h) - f(x)]/h=[(1/(x+h)-1/x]/h=[(x-(x+h))(x(x+h))]/h=-1/(x(x+h))

    Also, what exactly is the slope of the secant line?

    What is a secant line anyway?
    Definition of a secant line can be found here.

    As it is a line its slope is defined as the tan of the angle that
    the line makes with the horizontal.

    RonL
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  3. #3
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    Quote Originally Posted by symmetry View Post
    The slope of the secant line can be written this way:

    f(x + h) - f(x)/h.

    For both questions below, express the slope of the secant line of each function in terms of x and h. Be sure to simplify your answer.

    (1) f(x) = -3x + 2

    (2) f(x) = 1/x

    Also, what exactly is the slope of the secant line?

    What is a secant line anyway?
    Expanding on what CB said;

    It's known as the difference quotient of f.

    Given (x, f(x)) and (x + h, f(x + h)), then y = f(x) can be given by:

    [f(x + h) - f(x)]/[(x + h) - x] = [f(x + h) - f(x)]/h, where h does not equal 0.

    It's also the derivative (slope), which I recall you telling TPH you hadn't got to yet. Or, (y_2 - y_1)/(x_2 - x_1), or (delta y)/(delta x).
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  4. #4
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    ok

    Thank you both for your replies and the great math data given to me for my study time this coming week.
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