Can thresholds be modeled as weights?
In this example, you have 2 classes which are separated with a line with negative slope (if you don't know why please comment). So if you set the slope as +1 then you can not separate classes. The whole point is to learn the line and line is defined with its coefficients (including threshold but threshold is JUST ONE OF THEM!).

PS: If you later want to upgrade to multilayer perceptron and use backpropagation algorithm, then you need to choose randomly different initial weights for mathematical reasons according to the backpropagating error of layers