# How do you write an equation that contains points (-2, -3) and is perpendicular to 5x-2y=8?

May 27, 2018

color(brown)(2x + 5y = -19

#### Explanation:

Given equation is $5 x - 2 y = 8$

Writing it in Slope-intercept form,

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

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

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

Equation of line passing through (-2,-3) with slope -(2/5) is

$y + 3 = - \left(\frac{2}{5}\right) \cdot \left(x + 2\right)$

$5 y + 15 = - 2 x - 4$

color(brown)(2x + 5y = -19