What is the equation of the line that pa Isses through (-2, - 3) and is perpendicular to 2x - 3y = 6?

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