Answer: [tex]\dfrac{-1}{2}[/tex]
Step-by-step explanation:
The standard equation of a line in intercept form is given by :-
[tex]y=mx+b[/tex], where m is the slope of the line. (1)
Given equation of a line : [tex]2x-y=16[/tex]
It can be written as :
[tex]y=2x-16[/tex]
By comparing to the equation (1) , we have
[tex]m=2[/tex]
Also, the product of slopes of two perpendicular lines is -1.
Let p be the slope of the line perpendicular to [tex]2x-y=16[/tex], then we have
[tex]p\times 2=-1\\\\\Rightarrow\ p=\dfrac{-1}{2}[/tex]
Hence, the slope of the line perpendicular to [tex]2x-y=16[/tex] = [tex]\dfrac{-1}{2}[/tex]
