Why Perceptron Neurons Need Bias Input?

So, it is easy to notice that with b 0, the function will always pass through the origin [0,0]. And when we introduced values to b keeping a fixed, the new functions will always be parallel to each other. So, what could we learn from it? We can say that a component determines the angulation of the function, while the b component determines where the function cuts the x-axis. I think you already noticed the problem in that, right?