Question 1016058
A radius of the circle with endpoint (9,4) and the center (6,9) is on the line passing through those two points.  Omitting that set of steps, this radius is on the line {{{y=-(5/3)x+19}}}, showing the slope is  {{{-5/3}}}.


To answer the question for the exercise, you want the equation of the line with slope  {{{3/5}}} and passing through  (9,4).  The line will be TANGENT to {{{y=-(5/3)x+19}}} and will contain the point (9,4).,   
this way...
{{{y-4=(3/5)(x-9)}}} using point-slope form.
{{{y-4=(3/5)x-27/5}}}
{{{y=(3/5)x-27/5+4}}}
{{{y=(3/5)x-27/5+20/5}}}
{{{highlight(y=(3/5)x-7/5)}}}