Final answer:
The equation of the line perpendicular to 4x + 3y = 9 and passes through (-2, 3) is 3x - 4y = -18.
Step-by-step explanation:
To find the equation of a line that is perpendicular to the given line, we need to find the negative reciprocal of the slope of the given line. The given line's equation is 4x + 3y = 9, which can be rewritten as y = (-4/3)x + 3. The slope of this line is -4/3, so the perpendicular line will have a slope of 3/4.
Using the equation y - y1 = m(x - x1) with the point (-2, 3), we can substitute the values and the slope into the equation. This gives us y - 3 = (3/4)(x + 2).
After simplifying, the equation becomes 3x - 4y = -18. So, the perpendicular line that passes through (-2, 3) is represented by the equation 3x - 4y = -18, which is option A.