$16$ points$)$ Consider the perceptron in two dimensions: h $($x$)=$ sign wT x where w $=$

$[$w$0,$ w$1,$ w$2]$T and x $=[1,$ x$1,$ x$2]$T $.$ Technically, x has three coordinates, but we call this

perceptron two$-$dimensional because the first coordinate is fixed at $1.$

$($a$)(10$ points$)$ Show that the regions on the plane where h $($x$)=+1$ and h $($x$)=1$ are

separated by a line. If we express this line by the equation x$2=$ ax$1+$ b$,$ what are the

slope a and intercept b in terms of w$0,$ w$1,$ w$2?$