First, simplify the equation into slope-intercept form to make things easier. Slope-intercept form: y = mx + b
-9x - 6y = 8
-6y = 9x + 8
y = -9/6 - 8/6
y = -3/2 - 4/3
A line perpendicular to this would have a slope that is the negative reciprocal of the first slope. So, just flip the numerator and denominator and change to the opposite sign.
-3/2 becomes 2/3 (new slope)
A line parallel to this would have the same slope (-3/2).
