Calculate a new range from given range of values of unequal length I have an $x$ value increasing from $340$ to $640$, and I want an $s$ value to move from $1$ to $0.5$ based on the $x$ value.
So I'm wondering, how can I achieve this? 
I can get the first value in the range by dividing $340/340 = 1,$ but I don't know how to get to $0.5$ when $x$ is $640.$
 A: Conditions:  
$s(340) = 1$
$s(640) = 0.5$
linear (Actually affine)
To fit these conditions, first, take the starting points -- 340 and 640. As the difference is 300, an increase of 300 in x has to correspond to a decrease of 0.5 in s. Thus, the slope of the line will be $\frac{\Delta s}{\Delta x} = \frac{-0.5}{300} = -\frac{1}{600}$.
Now, taking the equation $s(x) = -\frac{x}{600} + b$ and solving for $b$ with the condition that $s(340) = 1$ gives that $1 = -\frac{340}{600} + b$, or $b = \frac{940}{600} = \frac{47}{30}$.
Thus, the resultant equation will be $s(x) = -\frac{x}{600} + \frac{47}{30}$. (Or, if you prefer to only have one fraction, $s(x) = \frac{940 - x}{600}$.)
Edit: It's also pretty easy to verify this afterwards. For example, $s(340) = \frac{940 - 340}{600} = \frac{600}{600} = 1$, and $s(640) = \frac{940 - 640}{600} = \frac{300}{600} = \frac{1}{2} = 0.5$.
A: \begin{align}
\text{Assuming a linear relationship}\\
s&=mx+c\\
1&=340m+c\\
0.5&=640m+c\\
\text{Solving simultaneous equations,}\\
m&=-0.0017=\frac{1}{600}\\
c&=1.5667=\frac{940}{600}
\end{align}
