The equation of line xy is (y−3) = negative 2 over 3(x − 4). what is the slope of a line perpendicular to xy?

The slope of line XY: m = - 2/3
The slope of a line perpendicular to XY:
m1 = 
m 1 = 1.5

The equation is:
y − 3 = −2/3(x−4)
y - 3 = -2/3x + 8/3
y = -2/3x + 17/3

Here, the slope is -2/3.
The slope of a line that is perpendicular to a line is the negative reciprocal of that slope.

We have -2/3 as the slope. The negative reciprocal is 3/2.

So the slope of a line perpendicular to XY is 3/2.