How do I write an equation using only one variable that could be used to solve for the constant variation of k?
How the equation is developed will depend upon the information provided.
A biologist counted the number of white tail deer in a 90 acre parcel of land in a nature preserve and found 10 deer. Find the constant of variation k.
From just the information provided, there isn't enough for an equation. You could set up a ratio
between the number of deer and the number of acres, to get a "deer per acre" rate, but that's about it. Unless they tell you more, such as "Assume that this parcel is representative, assume that the population varies directly as the area, and develop an equation which would model the population d of deer on an area of a acres", there's nowhere to go with this. Sorry!