What is the equation for the translation of x^2+y^2=9 four units to the right and three units down

We know that
X²+y²=9 -------> X²+y²=3²
is the equation of a circle with center (0,0) and radius r=3 units
so
the translation of four units to the right and three units down is equals to move the center (0,0)--------> (0+4,0-3)------> (4.-3)

the new center of the circle is (4,-3)
the new equation is
(x-4)²+(y+3)²=3²

see the attached figure

Ais the answer for your question

The linear equation is: y=ax+b