Question

If a line through the origin has a slope of 2, what is the slope of the line through the origin that is perpendicular to

it?

Answer 1

`-(1)/(2)`

Explanation:

We have the slope value of the first line, we will call this
`m_(1)`

so
`m_(1)=2`

And we use the condition so that two lines are perpendicular: the product of the two slopes must be equal to -1.

That is, if the slope of the first line is
`m_(1)` and the slope of the second line is
`m_(2)`:

`m_(1*)m_(2)=-1`

we know that
`m_(1)=2`, so:

`2m_(2)=-1`

and clearing for
`m_(2)`:

`m_(2)=-(1)/(2)`

the slope of the line perpendicular to the line with a slope of 2 is:
`-(1)/(2)`