[Coordinate method on the plane $]$

Form the equation of the line passing through the point $M(-3 ; 2)$ parallel to the line $2 x-3 y+4=0$.

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Let's write the equation of the given line as $y=\frac{2}{3} x+\frac{4}{3}$. Since the required line is parallel to the given one, its slope is equal to the slope of the given line, i.e., $\frac{2}{3}$. Therefore, the equation of the required line is $y=\frac{2}{3} x+l$.

Since the point $M(-3 ; 2)$ lies on this line, its coordinates satisfy the obtained equation, i.e., 2 = $\frac{2}{3} \cdot(-3)+l$ is a true equality. From this, we find that $l=4$. Therefore, the required equation is $y=\frac{2}{3} x +4$ or $2 x-3 y+12=0$.

## Answer

$2 x-3 y+12=0$.