3.2. Obtain the equation of the line passing through the point $P(-1 ; 2)$ and parallel to the vector $\ddot{a}=\{l ; m\}=\{8 ;-4\}$.
Solution.

1st step. Make a schematic drawing (Fig. 3.2).

2nd step. Write down the coordinates of the vectors defining the given geometric object - the line. These are the direction vector of the line $\vec{a}=\{l ; m\}=\{8 ;-4\}$ and the current vector $\widehat{P M}=\{x+1 ; y-2\}$.

3rd step. Write down one of the conditions - orthogonality or collinearity, according to the problem. According to the problem, $\overrightarrow{P M} \| \vec{a}$, so we will use the condition of collinearity of two vectors in coordinate form $(x+1) / 8=(y-2) /-4$. We obtain the canonical equation of the line.