f(-5) = -4, and f(5)= 2 linear equation satisfying the conditions , if possible

Question

f(-5) = -4, and f(5)= 2
linear equation satisfying the conditions , if possible

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RuslanHeatt 6 months 2021-09-01T16:10:06+00:00 1 Answers 6 views 0

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    2021-09-01T16:11:12+00:00

    Given:

    f(-5) = -4, and f(5)= 2.

    To find:

    The linear equation satisfying the conditions.

    Solution:

    We have,

    f(-5) = -4, and f(5)= 2

    It means the function passes through the points (-5,-4) and (5,2). So, the linear equation of the function f is

    y-y_1=\dfrac{y_2-y_1}{x_2-x_2}(x-x_1)

    y-(-4)=\dfrac{2-(-4)}{5-(-5)}(x-(-5))

    y+4=\dfrac{2+4}{5+5}(x+5)

    y+4=\dfrac{6}{10}(x+5)

    On further simplification, we get

    y+4=\dfrac{3}{5}(x+5)

    y+4=\dfrac{3}{5}x+3

    y=\dfrac{3}{5}x+3-4

    y=\dfrac{3}{5}x-1

    Putting y=f(x), we get

    f(x)=\dfrac{3}{5}x-1

    Therefore, the required function is f(x)=\dfrac{3}{5}x-1.

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