How this calculator works
Two distinct x coordinates define a linear model. The target position along the x interval supplies the same fraction of the change in y. Reverse modes rearrange this relation to recover a target x or one missing reference coordinate. A zero coefficient means the inverse is not unique and is rejected. Values outside the reference interval are extrapolations, which may be poor estimates of a curved relationship.
Formula
y = y1 + (x - x1)(y2 - y1)/(x2 - x1); m = (y2-y1)/(x2-x1); b = y1 - m x1.
Worked example
Between (0, 10) and (10, 30), x = 5 is halfway along the interval, so y = 20. The line has slope 2 and intercept 10. At x = 15 it extrapolates to y = 40.
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Frequently asked questions
Can the points be entered backwards?
Yes. Reversing both point pairs leaves the line and estimate unchanged.
Why reject equal x coordinates?
They cannot define y as a single-valued linear function of x.
Is interpolation exact?
It is exact for the straight-line model. Real data between observations may follow a different curve.