Question 391825
In order to find a perpendicular line, you need the equation in the form: {{{y=mx+b}}}

So convert your function into the form mentioned above:
{{{3x-(1/5)y=3}}}
={{{(-1/5)y=3-3x}}}
={{{y=15x-15}}}

Next, we take the inverse reciprocal of the slope (m is the slope in the equation y=mx+b.

The reciprocal of 15 is 1/15, to invert the number, simply make it the opposite sign that it currently is (positive turns to negative, and vice-versa).  Therefore, the slope of the line perpendicular to y=15x-15, is -1/15.
The perpendicular line, now has the equation:  {{{y=(-1/15)x+b}}}
Now, we must solve for b.  To solve for b, we simply plug in the x and y values from the point above.  (x,y), (6,-5).

{{{-5=(-1/15)(6)+b}}}
{{{-5=-6/15+b}}}
{{{-5+6/15=b}}}
{{{-75/15+6/15=b}}}
{{{-69/15=b}}}

Now plug b back into the equation and you have your answer:
{{{highlight(y=(-1/15)x-69/15)}}}