Analogy:
Imagine you’re making a decision about whether to go out for a movie .

You consider three things:

• Money (do I have enough?)
• Time (am I free?)
• Mood (do I feel like it?)

But not all things are equally important.

• Money might matter the most (high weight).
• Time might matter a little less.
• Mood might matter the least.

 So, you multiply each factor by its importance (weight), and then add them all up.

That adding and weighing is what we call a linear transformation in ANN.
It’s just: combine all inputs with their importance.

 In math:

z=w1x1+w2x2+…+wnxn+b

The weights × inputs decide how strong each input is.

The bias (b) shifts the result up or down.