Final answer:
The slope of any line perpendicular to AB is 3/2.
Step-by-step explanation:
To find the slope of any line perpendicular to AB, we need to find the slope of line AB first. The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
For the points A(2, -3) and B(-4, 1), the slope of line AB is:
slope = (1 - (-3)) / (-4 - 2) = 4/(-6) = -2/3
Therefore, any line perpendicular to AB will have a slope that is the negative reciprocal of -2/3. The negative reciprocal of -2/3 is 3/2. So, the slope of any line perpendicular to AB is 3/2.