The point slope form is Y- Y1 = m(X - X1)
where m is the slope
and Y1 and X1 are the x and y values of a point on the line.
It this case y = x +2 is in the slope intercept form so we know that the slope = 1 (coefficient of x)
and the point (0,2) is a point on the line (intercept)
therefore
Y -2 = X - 0
or Y -2 = X is the point slope form of the line