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

Jul 11, 2018

$\text{perpendicular slope } = - 2$

#### Explanation:

$\text{calculate the slope m using the "color(blue)"gradient formula}$

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(-17,23)" and } \left({x}_{2} , {y}_{2}\right) = \left(21 , 25\right)$

$m = \frac{25 - 23}{21 - \left(- 17\right)} = \frac{2}{38} = \frac{1}{19}$

$\text{the slope of any perpendicular line is}$

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

$- 19$

#### Explanation:

The slope $m$ of straight line joining $\left({x}_{1} , {y}_{1}\right) \setminus \equiv \left(- 17 , 23\right)$ & $\left({x}_{2} , {y}_{2}\right) \setminus \equiv \left(21 , 25\right)$

$m = \setminus \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$= \setminus \frac{25 - 23}{21 - \left(- 17\right)}$

$= \frac{1}{19}$

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)

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

$= - \frac{1}{\frac{1}{19}}$

$= - 19$