"Point slope" is not either y= x- 3 or x= y+ 3. Point slope is \(\displaystyle y- y_0= m(x- x_0)\), where m is the slope and \(\displaystyle (x_0, y_0)\) is a point the line goes through. Here that would be \(\displaystyle y- 0= 1(x- 3)\).
Slope intercept:
the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept
point slope:
the equation of a straight line in the form y − y1 = m(x − x1) where m is the slope of the line and (x1, y1) are the coordinates of a given point on the line