To make the equation go through (0,-4) the new equation would be 9x + 5y = 20. We needed to change it from subtracting to adding so the direction of the line would go from going down to up too up to down. In slope-intercept form the original equation would be found by the following.
9x - 6y = 20
-6y = 20 - 9x
y = -20/6 - (-9/6x)
y = 9/6x - 20/6
y = 3/2x - 10/3
To make the perpendicular line, take the slope and apply the opposite and reciprocal.
y = -2/3x - 10/3
Best of Luck!
