Question

What is the slope of any line perpendicular to the line passing through `(-17,23)` and `(21,25)`?

Answer 1

`"perpendicular slope "=-2`

Explanation:

`"calculate the slope m using the "color(blue)"gradient formula"`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(-17,23)" and "(x_2,y_2)=(21,25)`

`m=(25-23)/(21-(-17))=2/38=1/19`

`"the slope of any perpendicular line is"`

`•color(white)(x)m_(color(red)"perpendicular")=-1/m=-1/(1/19)=-19`

Answer 2

`-19`

Explanation:

The slope `m` of straight line joining `(x_1, y_1)\equiv(-17, 23)` & `(x_2, y_2)\equiv(21, 25)`

`m=\frac{y_2-y_1}{x_2-x_1}`

`=\frac{25-23}{21-(-17)}`

`=1/19`

We know that the product of slope of two perpendicular lines is `-1` then the slope #`of the straight line perpendicular to the given line joining`(-17, 23)`&`(21, 25)#

`=-1/m`

`=-1/(1/19)`

`=-19`