Finding value of theta in linear classification
Since it is an exam question, I will give you hints and leading questions instead of answers.
Note that $x^T w$ must be well-defined, and $x$ is 2-dimensional. What is the dimension of $w$?
How is bias incorporated into the model?
The margin satisfies $\widehat{y} = 0.$ What is the equation of the margin (as a function of x and bias)?
P.S. I expect a typo/vagueness in this question.