How do you write the equation in point slope form given (4, -5), perpendicular to 2x-5y= -10?

May 25, 2018

Equation in point slope form of the perpendicular line and passing through point $\left(4 , - 5\right)$ is

color(indigo)(y + 5 = -(5/2) (x-4)

Explanation:

$2 x - 5 y = 10$

$5 y = 2 x - 10$

$y = \left(\frac{2}{5}\right) x - 2$

Slope of the line $m = \left(\frac{2}{5}\right)$

Slope of the perpendicular line $= - \left(\frac{1}{m}\right) = - \left(\frac{5}{2}\right)$

Equation of line with slope $- \left(\frac{5}{2}\right)$ and passing through point $\left(4 , - 5\right)$ is

color(indigo)(y + 5 = -(5/2) (x-4)