Question 252784
The equation of the given line is -3x+5y = 5 ...(1)
The equation of a line parallel to this line is -3x+5y = k ...(2) 
where k is a constant.
We are given that this line passes through the point(4,-5)
Put x=4 and y=-5 in (2)
We get,  -3*4+5*(-5) = k
          -12-25 = k
               k = -37
Therefore,the equation of a line parallel to the given line through the point(4,-5)is -3x+5y = -37  or 3x-5y=37   ....(3)
 
Next, the equation of a line perpendicular to the given line is 5x+3y = c ..(4)
where c is a constant.
We are given that this line passes through the point(4,-5)
Put x=4 and y=-5 in (4)
We get,  5*4+3*(-5) = c
          20-15 = c
              c = 5
Therefore,the equation of a line perpedicular to the given line through the point(4,-5)is 5x+3y=5   ....(5)