Chew. please, a children's problem on proportions?

Question

Mathematics

There is a dependence of temperature on altitude (not in the real world).

256: 10.0
For example 100: ?
64:24.0

But that's not the same as just:
256:10.0
100: ?

Since there is also the last ratio and it can be set to anything, even 64:2. I still don't quite understand what it's called.

So far, I've been trying to think like this:
I imagine this as a kind of change over time. Altitude from 256 to 64, and temperature from 10 to 24.
So 192/14=13.7 is the rate of change of meters per degree.
So if we need 100, it's 156/13.7=11.3.
So 24-11.3=12.7.... probably from a larger number... But further there in the table, the values ​​​​can also change vice versa in plus, etc., such as a gradient.

I'm confused :( Yes, yes, they already answered me "What's the question?", "Well, solve the simple proportion of the 5th grade", "Well, you yourself named the answer" and other useful answers. Therefore, I ask you honestly - chew it, please, I'm a moron)) Surely there is a formula. I know about linear interpolation, but only when 0 and 1 on the other side.

Answer 1

You misunderstand the problem.
You have only two values, so without further ado you can assume that in the area [64, 256] you have a linear relationship. It is enough to solve the system:
64a + b = 24
256a + b = 10
As a result, we get the dependence -0.073
* x + 28.667 = y
at 100 m will be approximately
21.367
An-1*x1^(n-1) ... A1*x1 + A0 = y1
An*x2^n + An-1*x2^(n-1) ... A1*x2 + A0 = y2
.. ................................................. ..............
An*xn^n + An-1*xn^(n-1) ... A1*xn + A0 =
yn function