Answer: a) \(y-2=\dfrac{3}{2}(x-3)\), b) \(y-2=-\dfrac{2}{3}(x-3)\)
Solution: First, we need to know the slope of our given line.
\[5+6x-4y=0\]
\[5+6x=4y\]
\[\dfrac{5}{4}+\dfrac{3}{2}x=y\]
a) The slope of the given line is \(\dfrac{3}{2}\), so the parallel line for a) will also have a slope of \(m=\dfrac{3}{2}\).
\[y-2=\dfrac{3}{2}(x-3)\]
b) The perpendicular slope will be \(m_{\perp}=-\dfrac{2}{3}\), so the equation of the perpendicular line will be
\[y-2=-\dfrac{2}{3}(x-3)\]