Answer:
The equation of the line would be y = -3/2x + 19/2
Explanation:
First we need to solve the original equation for y so that we can find the slope.
2x - 3y = 0
-3y = -2x
y = 2/3x
So since the equation has a slope of 2/3, we know the perpendicular slope would be -3/2 (since perpendicular slopes have opposite and reciprocal slopes). Then we can use this and the ordered pair in point-slope form.
y - y1 = m(x - x1)
y - 5 = -3/2(x - 3)
y - 5 = -3/2x + 9/2
y = -3/2x + 19/2