On the Wikipedia Bilinear interpolation page there is this numerical example. I am talking about the example with this image.
There I see $I_{20,14.5}=\frac{15-14.5}{15-14} \cdot 91 + \frac{14.5-14}{15-14} \cdot 210$
Should not we swap $91$ and $210$, as $210$ is the intensity of column $15$?
I believe that formula is correct. Thinking about the endpoints, if we replace 14.5 by 15, then the result is
$$ \frac{15-15}{15-14}\cdot 91 + \frac{15 - 14}{15 - 14}\cdot 210 = 0 \cdot 91 + 1 \cdot 210 = 210 $$
and at 14, the result is
$$ \frac{15-14}{15-14}\cdot 91 + \frac{14 - 14}{15 - 14}\cdot 210 = 1 \cdot 91 + 0 \cdot 210 = 91 $$
These should make sense: 15 does have value 210 and 14 does have value 91.
Values between 14 and 15 linearly interpolate between 210 and 91.
You can think of $\frac{t-14}{15-14}$ (the second fraction) as meaning "the percentage $t$ has completed along its journey from 14 to 15". When this number is close to 0, you want the result to be close to the value for 14 (which is 91). When this result is close to 1, you want the result to be close to the value for 15 (Which is 210).