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HomertheGenius
The slope of line XY: m = - 2/3
The slope of a line perpendicular to XY:
m1 = [tex] \frac{-1}{ \frac{-2}{3} }= \frac{3}{2} [/tex]
m 1 = 1.5
Hagrid
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.