is the relationship between the variables in the table a direct variation, an inverse variation, or neither? if it is a direct or inverse, w

Question

is the relationship between the variables in the table a direct variation, an inverse variation, or neither? if it is a direct or inverse, write a function to model it. x-9,11,13,15- y- -17, -1,6,27

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    2021-09-22T18:12:45+00:00

    Answer:

    The relation is neither a direct variation nor an inverse variation.

    Step-by-step explanation:

    We will say a relation is direct variation, if increase in one variable causes the other variable to increase and the two variables need to satisfy y=kx else for an increase in variable ,if there is decrease in other variable and the two variables has to satisfy y=\frac{k}{x}, then it is called inverse variation.

    Let us compare the x and y-values in the table.

    x is increasing from 9 to 11 to 13 to 15.

    And y is also increasing from -17 to -1 to -6 to 27.

    Hence the relation is not definitely inverse variation but may be direct variation. Let us check it by finding k for x=9 and x=11.

    For x=9, y=-17 that is -17=k(9)

                                      k=\frac{-17}{9}

    For x=11, y=-1 that is -1=k(11)

                                    k=\frac{-1}{11}

    Since k is different for different pairs it is not direct variation also.

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