Answer
$3x-2y=4$
Work Step by Step
The result of exercise 32 tells us that ${\bf v}=a{\bf i} + b{\bf j}$
is parallel to the lines $bx-ay=c$
Here, ${\bf v}=2\cdot{\bf i} + 3\cdot{\bf j}$,
$a=3,\quad b=3,$
and the lines are $3x-2y=c.$
$P(0,-2)$ is on the line $\Rightarrow \left\{\begin{array}{l}
3(0)-2(-2)=c\\
c=4
\end{array}\right.$
so the line equation is $\quad 3x-2y=4$
(a second point on the line is $(2,1)$ )
