I'm building a model but I got stuck at this:
I have $x,y$ whose ranges are ($10,000$ to $2,000,000$) and (1 to 36) respectively. Also I have a z that ranges from 16 to 30. I know their relations in certain cases. I know that when:
Case 1: $X=10,000$ and $Y=1$ then $Z=16$ //When $X$ and $Y$ are at their lower ranges, then $Z$ is at it's low
Case 2: $X=2,000,000$ and $Y=36$ then $Z=30$ //When $X$ and $Y$ are at their top ranges, then $Z$ is at it's top
Case 3: $X=1,005,000$ and $Y=18.5$ then $Z=23$ //The middle
Given this how could I make an equation system correctly that given $X$,$Y$ I get $Z$?
I tried using case 1 and 2 for a two variable solution (using $Z$ as a constant, didn't worked), then I tried using the three cases as equations but the same. Don't know if this is too low level for this site but google searches gave me no clue.
Basically, you have these two points (we don't need the 3rd)
$(10000,1,16)$ and $(2000000,36,30)$
you can think of it this way:
$$z = \alpha x + \beta y$$ $$16 = \alpha * 10000 + \beta $$ $$30 = \alpha * 2000000 + \beta *36$$
Solve for $\alpha$ and $\beta$ ($\frac{-273}{820000}$ and $\frac{1585}{82}$ respectively I think)
Then, you're done.