For this case we have to by definition, if two lines are perpendicular then the product of its slopes is -1.
That is to say:
[tex]m_ {1} * m_ {2} = - 1[/tex]
We have the following equation:
[tex]y = -2x + 8[/tex]
So:
[tex]m_ {1} = - 2[/tex]
Thus:
[tex]m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {- 2}\\m = \frac {1}{2}[/tex]
Thus, a line perpendicular to the given line must have slope [tex]m = \frac {1} {2}.[/tex]
Option A:
[tex]x + 2y = 8\\2y = -x + 8\\y = - \frac {1} {2} x + 4[/tex]
It is not perpendicular!
Option B:
[tex]x-2y = 6\\2y = x-6\\y = \frac {1} {2} x-3[/tex]
If it is perpendicular!
Option C:
[tex]2x + y = 4\\y = -2x + 4[/tex]
It is not perpendicular!
Option D:
[tex]2x-y = 1\\y = 2x-1[/tex]
It is not perpendicular!
The correct option is option B
ANswer:
Option B
