How do you write an equation of a line passing through (4, -5), perpendicular to 2x-5y= -10?

Apr 8, 2018

color(green)("Equation of the perpendicular line is "

color(crimson)(5x + 2y = 10

Explanation:

$2 x - 5 y = 10$

$- 5 y = - 2 x + 10$

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

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

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

$\text{Equation of line 2 is given by } \left(y - {y}_{2}\right) = m \cdot \left(x - {x}_{2}\right)$

$\left(y - \left(- 5\right)\right) = - \left(\frac{5}{2}\right) \cdot \left(x - 4\right)$

$2 y + 10 = - 5 x + 20$

$5 x + 2 y = 10$