Constant variation of K = Huh?

[HotelPaper]

My teacher submitted a problem to us that I don't understand. I'll c/p the word problem so you can see what I'm talking about:

"To estimate animal populations, biologists count the total number of animals in a small section of a habitat. The total population of animals is directly proportional to the size of the habitat (in acres) polled.

Write an equation using only one variable that could be used to solve for the constant of variation k."

I've looked in my text book but I'm at a loss how to set this up.

Or how to set up part b.

"A biologist counted 12 white tail deer in a 100-acre parcel of land in a nature preserve. Find the constant of variation k."

I'm not sure what the 'constant variation of k' is or how to put part b into the equation.

Please help?

 

[Loren]

Suppose we know that y is always 3 times as big as x. Therefore, we know that y = 3x.

But, what if we don't know the relationship between x and y but do know that the relationship does not change? So, if we find a value for x and a value for y that occur at the same time we can write the equation...

y = kx, where k represents some constant.

Now, suppose we find that when x = 10, y = 5. (This is different than what is proposed above.)

Since y=kx, we can substitute those values into our known equation and get

5 = k(10) or 5 = 10k
Solving for k we find that k = 1/2

Therefore, our original equation becomes y = (1/2)x.

Now, if we can calculate the value of y for any given x, and visa versa.

If x = 30, y=(1/2)30= 15.
If y = 7, 7=(1/2)x so x=14.