# What is the equation of a line that passes through the point (10, 5) and is perpendicular to the line whose equation is y=54x−2 ?

Jun 29, 2018

Equation of line with slope $- \frac{1}{54}$ and passing through $\left(10 , 5\right)$ is

color(green)(x + 54y = 280

#### Explanation:

$y = 54 x - 2$

Slope $m = 54$

Slope of perpendicular line ${m}_{1} = \frac{1}{-} m = - \frac{1}{54}$

Equation of line with slope $- \frac{1}{54}$ and passing through $\left(10 , 5\right)$ is

$y - 5 = - \left(\frac{1}{54}\right) \cdot \left(x - 10\right)$

$54 y - 270 = - x + 10$

$x + 54 y = 280$