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Option A.

Step-by-step explanation:

Simplifying

xy + -9z = 4

Solving

xy + -9z = 4

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '9z' to each side of the equation.

xy + -9z + 9z = 4 + 9z

Combine like terms: -9z + 9z = 0

xy + 0 = 4 + 9z

xy = 4 + 9z

Divide each side by 'y'.

x = 4y-1 + 9y-1z

Simplifying

x = 4y-1 + 9y-1z

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: