Question

What is the slope of a line perpendicular to this line? Y=3/4x

Answer 1

`-4/3`

Explanation:

Here

`y=mx`

is the given eq, with `m` being the slope of the given line. Therefore, the slope of this line is `3/4` `(m)`.

But the slope of the line perpendicular to the given line is `=-1/m`, so the answer is `=-1/(3/4)`

which is `=-4/3`.

Answer 2

The perpendicular slope is `-4/3`.

Explanation:

Given:

`y=3/4x`

The slope that is perpendicular to `3/4` is its negative reciprocal, which is `-4/3`.

Mathematically

`m_1m_2=-1`,

where `m_1` is the given slope and `m_2` is the perpendicular slope.

`3/4m_2=-1`

Multiply both sides by `4/3`.

`color(red)cancel(color(black)(4))^1/color(red)cancel(color(black)(3))^1xxcolor(red)cancel(color(black)(3))^1/color(red)cancel(color(black)(4))^1m_2=-1xx4/3`

Simplify.

`m_2=-4/3`