Question 85231
 The slopes of parallel lines is always equal.

In the equation  2x + 3y = 7   let us find the slope
     3y = 7-2x
      y = 7/3 -2/3 x
 Now the equation is in the form y = mx +c 
where m= ,slope which is the coefficient of x
 so we get m= -2/3
We'll use m=-2/3 & the coordinates (6,5) to get the equation of the line.
(since the line goes through the point (6,5) the values of x & y will satisfy the equation. )
   y = mx + c
   5 = -2/3 * 6 + c
   5 = -4 + c
   9 = c
The eq of the line becomes
  y = -2/3 + 9
 Multiplying by 3 on both sides
  3y = -2x + 27
  3y +2x = 27

the answer is :    3y + 2x = 27