Differentiate wrt x: 2(x+5)+2(y-9)dy/dx=0. At (-13,-6) we have -16-30dy/dx=0, so dy/dx=-16/30=-8/15. This is the slope of the tangent line y=mx+b where m=dy/dx=-8/15. -6=-8/15*(-13)+b is the tangent line at (-13,-6). So -6=104/15+b, making b=-194/15 and y=-(8x+194)/15, which can be written: 15y+8x+194=0.