Question

How do you identify if the following as linear or nonlinear y=5x-4?

Answer 1

It's not linear.

Explanation:

If `f` were linear then `f(lambda a) = lambda f(a) and f(a + b) = f(a) + f(b)`

but `f(x) = 5x - 4 => f(lambda x) = 5 lambda x - 4`
`ne lambda f(x) = 5 lambda x - 4 lambda`

also

`f(a + b) = 5(a + b) -4 ne f(a) + f(b) = 5a - 4 + 5b - 4`