Answer
(a) $-\frac{1}{2}$
(b) $-\frac{7}{2}$
Work Step by Step
(a) As the line is parallel to $3y+2x=6$, the slope is $m=-\frac{2}{3}$, we have $\frac{2-(-1)}{k-4}=-\frac{2}{3}$ which gives $k=-\frac{1}{2}$
(b) As the line is perpendicular to $2y-5x=1$ (which has a slope of $\frac{5}{2}$), the slope of the required line is $m=-\frac{2}{5}$, thus we have $\frac{2-(-1)}{k-4}=-\frac{2}{5}$ which gives $k=-\frac{7}{2}$
