# What is the slope of any line perpendicular to the line passing through (0,6) and (18,4)?

Mar 14, 2018

Slope of any line perpendicular to the line passing through

$\left(0 , 6\right) \mathmr{and} \left(18 , 4\right)$ is $9$

#### Explanation:

The slope of the line passing through $\left(0 , 6\right) \mathmr{and} \left(18 , 4\right)$

is ${m}_{1} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{4 - 6}{18 - 0} = \frac{- 2}{18} = - \frac{1}{9}$

The product of slopes of the perpendicular lines is ${m}_{1} \cdot {m}_{2} = - 1$

$\therefore {m}_{2} = - \frac{1}{m} _ 1 = - \frac{1}{- \frac{1}{9}} = 9$ . Therefore slope of any line

perpendicular to the line passing through $\left(0 , 6\right) \mathmr{and} \left(18 , 4\right)$

is $9$ [Ans]