The decision boundary of our previous network can be calculated by looking at the following condition
x1w1+x2w2=0
We can change the equation into
When we look at the general form of a straight line y=mx+b, we can easily see that our equation corresponds to the definition of a line and the slope (aka gradient) m is −w1w2 and b is equal to 0.
As the constant term b determines the point at which a line crosses the y-axis, i.e. the y-intercept, we can see that our network can only calculate lines which pass through the origin, i.e. the point (0, 0). We will need a bias to get other lines as well.