Question 18388
First, you need to write both equations in the slope-intercept form: {{{y = mx + b}}}

1) {{{3x + Ky = 2}}} Subtract 3x from both sides.
{{{Ky = -3x + 2}}} Divide both sides by K
{{{ y = (-3/K)x + 2/K}}} The slope is: {{{m = (-3/K)}}}

2) {{{6x - 5y - 1 = 0}}} Add 5y to both sides.
{{{6x - 1 = 5y}}} Divide both sides by 5.
{{{y = (6/5)x - 1/5}}} The slope is: {{{m = 6/5}}}

Since the lines are parallel, the slopes must be equal, as you have correctly noted.

{{{(-3/K) = 6/5}}} Solve for K. Multiply both sides by K.
{{{-3 = 6K/5}}} Multiply both sides by 5.
{{{-15 = 6K}}} Divide both sides by 6.
{{{(-15)/6 = K}}} Simplify.
{{{K = (-5/2)}}}