Keller’s third law of orbital motion states that you can approximate the period P(in earth years) it takes a planet to complete one orbit of the sun using the fraction P= D 2 over 3, where is the distance (in astronomical units, AU) from the planet to the sun. Howmany earth years would it take for a planet that is 200 AU from the sun?

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

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