Answer:
3x + 2y + 12 = 0
Step-by-step explanation:
1) Rewrite 2x - 3y = 6 as 2x - 6 = 3y. Then we know the slope of the desired line is (2/3).
2) Take the negative reciprocal of this, obtaining -3/2. This is the slope of any line which is perpendicular to 2x - 6 = 3y.
3) Use the slope-intercept form of the equation of a line, y = mx + b:
Replace y with -3, x with -2, and m with -3/2:
-3 = (-3/2)(-2) + b, or
-3 = 3 + b. Thus, b = -6, and the desired equation is y = (-3/2)x - 6, or
2y = -3x - 12, or
3x + 2y + 12 = 0
