80. A point $M_{1}(7 ; -8)$ and a normal vector of the line $\vec{n}=(-2 ; 3)$ are known. Form the equation of the line.
Solution. $1^{0}$. Choose a point $M(x ; y)$.

$2^{0}$. Find the vector $\overrightarrow{M_{1} M}=(x-7 ; y+8)$.

$3^{0}$. The normal vector $\vec{n}=(2 ; 3)$, i.e., $A=2, B=3$.

$4^{0}$. Write the equation of the desired line:

$$
2(x-7)+3(y+8)=0
$$

from which

$$
2 x-14+3 y+24=0 ; 2 x+3 y+10=0
$$

- the desired equation in general form.