Find an equation for the line tangent to the circle x^2 +y^2=25 at the point (3, -4)

Hello : 
the center of this cercle is : O( 0, 0)
calculate the slope  m of the line : OA    .. A (3,-4)
m= (yA - yO) / (xA- xO) 
m = (-4-0)/(3-0)
m= -4/3
if : k the slope of the tangent : k×m = -1   (the tangent perpendiclar of : OA)
k× (-4/3) = -1
k = 3/4
an equation of this tangent is : y - (-4) = (3/4)(x-3)

I’m not sure how this works