Question 748222
First, find the slope of:

{{{3x-5y = 2}}}

To do this, get the equation into slope-intercept form: y=mx+b

{{{3x-5y = 2}}}

Subtract 3x from both sides:

{{{-5y = -3x+2}}}

Divide both sides by -5:

{{{y = 3/5*x+2}}}

So the slope of that line is 3/5.  

When finding a perpendicular slope, just flip the slope and change the sign.  

So the perpendicular slope will be:

{{{-5/3}}}

Now, you have a point the line will be going through: (-5,6) and the slope: -5/3

As its name suggests, you'll be using Point-Slope form now to find the equation of the line.

{{{Y-Y1=M(X-X1)}}}

Plug the x and y from your ordered pair in for X1 and Y1.  Plug in -5/3 for m:

{{{Y-6=-5/3*(X-(-5))}}}

Subtracting a negative is like adding a positive...

{{{Y-6=-5/3*(X+5)}}}

Now we just have to distribute, and get this into slope-intercept form (y=mx+b)

{{{Y-6=-5/3*X-25/3))}}}

Add six to both sides:

{{{Y-6+6=-5/3*X-25/3+6}}}

{{{Y=-5/3*X-25/3+18/3}}}

{{{Y=-5/3*X-7/3}}}