Question

4. Which of the following lines is perpendicular to y = -2X + 8?

Answer 1

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:

$m_ {1} * m_ {2} = - 1$

We have the following equation:

$y = -2x + 8$

So:

$m_ {1} = - 2$

Thus:

$m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {- 2}\\m = \frac {1}{2}$

Thus, a line perpendicular to the given line must have slope $m = \frac {1} {2}.$

Option A:

$x + 2y = 8\\2y = -x + 8\\y = - \frac {1} {2} x + 4$

It is not perpendicular!

Option B:

$x-2y = 6\\2y = x-6\\y = \frac {1} {2} x-3$

If it is perpendicular!

Option C:

$2x + y = 4\\y = -2x + 4$

It is not perpendicular!

Option D:

$2x-y = 1\\y = 2x-1$

It is not perpendicular!

The correct option is option B

ANswer:

Option B