# What is the slope of a line that is perpendicular to 2x-5y=3?

Nov 6, 2017

$- \frac{5}{2}$

#### Explanation:

The slope of the given line can be determined by writing the equation in its slope-intercept form.

$2 x - 5 y = 3$

$- 5 y = 3 - 2 x$

$y = - \frac{3}{5} + \frac{2 x}{5}$
$y = \frac{2}{5} x - \frac{3}{5}$

The slope of the given line is $\frac{2}{5}$

The slope of the line perpendicular to the given line is equal to the negative reciprocal of the slope of the given line.

negative reciprocal of $n$ = $\frac{- 1}{n}$

negative reciprocal of $\frac{2}{5} = \frac{- 1}{\frac{2}{5}}$
$- \frac{1}{1} \div \frac{2}{5}$

$= - \frac{1}{1} \cdot \frac{5}{2}$

$- \frac{5}{2}$