9514 1404 393
Answer:
3x +2y +24 = 0
Explanation:
In general, the equation of a perpendicular line can be found by swapping the coefficients of x and y, then negating one of them. The value of the constant will be what is required to make the line pass through the given point.
The equation will be of the form ...
3x +2y +c = 0
At the given point, (x, y) = (-6, -3), we have ...
3(-6) +2(-3) +c = 0 . . . . substitute the given point coordinates
-18 -6 +c = 0 . . .simplify
c = 24 . . . . . . . . add 24
The general-form equation for the line is ...
3x +2y +24 = 0 . . . . . shown in blue in the attachment