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

Jul 6, 2017

It's not linear.

#### Explanation:

If $f$ were linear then $f \left(\lambda a\right) = \lambda f \left(a\right) \mathmr{and} f \left(a + b\right) = f \left(a\right) + f \left(b\right)$

but $f \left(x\right) = 5 x - 4 \implies f \left(\lambda x\right) = 5 \lambda x - 4$
$\ne \lambda f \left(x\right) = 5 \lambda x - 4 \lambda$

also

$f \left(a + b\right) = 5 \left(a + b\right) - 4 \ne f \left(a\right) + f \left(b\right) = 5 a - 4 + 5 b - 4$