Question

For linear equation: y=ax+b

a, x and b all have error. How to do the error propagation associated with y.

Answer 1

See this example:

Example: x = (2.0 ± 0.2) cm, y = (3.0 ± 0.6) cm. Find z = x - 2y and its uncertainty.

z = x - 2y = 2.0 - 2(3.0) = -4.0 cm Dz = Dx + 2 Dy = 0.2 + 1.2 = 1.4 cm So z = (-4.0 ± 1.4) cm.

Using Eq 1b, z = (-4.0 ± 0.9) cm.

The 0 after the decimal point in 4.0 is significant and must be written in the answer. The uncertainty in this case starts with a 1 and is kept to two significant figures.

So, here also

y = ax + b

dy = aDx + Db

So, y = (ax+b) ± (aDx + Db)