The graph shows the relationship between men’s shoe sizes and their heights. What tripe of relationship is this?

Dependent.

Step-by-step explanation: It would be dependent because you could be 5'4" and have a shoe size of 7 1/2. But if you're, let's say 6'0", you will have a bigger shoe size than someone who is shorter than you, for example your shoe size might be and 9 or 10, while the other person's might be only a 6 or a 7.

A) a linear relationship showing as height increases, shoes size increases

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:

step-by-step explanation: