Question

What is the slope of any line perpendicular to the line passing through `(-2,6)` and `(-7,4)`?

Answer 1

Slope of the perpendicular line `m_2=-5/2`

Explanation:

Given -

The two points on the given line.

`x_1=-2`
`y_1=6`
`x_2=-7`
`y_2=4`

Slope of the given line `m_1`

`=(y_2-y_1)/(x_2-x_1)=(4-6)/(-7-(-2))=(-2)/(-5)=2/5`

Slope of the perpendicular line `m_2`

Two line are perpendicular if `(m_1 xx m_2=-1)`

Find `m_2`

`2/5 xx m_2= -1`
`m_2=-1 xx 5/2=-5/2`

Answer 2

`-5/2`

Explanation:

Find slope of line through points using formula `(y_2 -y_1 )/(x_2 -x_1)`. Slope of a line perpendicular to a given line is the negative reciprocal.