Answer:
Option D: [tex]\frac{3}{2}[/tex] is the correct answer.
Step-by-step explanation:
Given points are:
P(-8,5) and Q(-2,1)
Slope is the steepness of a straight line.
We will find slope of PQ
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{1-5}{-2-(-8)\\m=\frac{-4}{-2+8}\\m=\frac{-4}{6}\\m=\frac{-2}{3}[/tex]
The product of slopes of two perpendicular lines is equal to -1.
Let,
x be the slope of other line.
m.x = -1
[tex]\frac{-2}{3}x=-1\\x=\frac{3}{2}[/tex]
Therefore,
The slope of a line perpendicular to the line PQ is [tex]\frac{3}{2}[/tex].
Hence,
Option D: [tex]\frac{3}{2}[/tex] is the correct answer.
