Determine whether y varies directly with x. If so find the constant of variation k and write the equation. X 4,7,10,13. Y 6.4,11.2,16,20.8

Question

Determine whether y varies directly with x. If so find the constant of variation k and write the equation. X 4,7,10,13. Y 6.4,11.2,16,20.8

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Alaia 4 months 2022-01-24T01:00:10+00:00 2 Answers 0

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    0
    2022-01-24T01:01:44+00:00

    Answer:k=1.6

    Step-by-step explanation:

    Let us suppose

    y=Kx

    so satisfying the point \left ( 4,6.4\right )

    k=\frac{6.4}{4}=1.6

    For \left ( 7,11.2\right )

    k=\frac{11.2}{7}=1.6

    For \left ( 10,16\right )

    k=\frac{16}{10}=1.6

    for \left ( 13,20.8\right )

    k=\frac{20.8}{13}=1.6

    thus y varies linearly with x.

    0
    2022-01-24T01:01:48+00:00

    Direct variation is modeled by

    … y = k·x

    Then the value of k can be found by finding the ratio of any corresponding pair of numbers from your table. I find it convenient to choose the one where x=10, so the math is easy to do mentally.

    … y/x = k

    … 16/10 = k = 1.6

    Then the equation is

    y = 1.6x

    _____

    Checking the other values in the table, we find that this equation fits all of them, so you do have direct variation.

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