# How do you find the slope of a line perpendicular to 5x-2y=-1?

Apr 1, 2015

Remember that given a slope, $m$, the slope perpendicular to it is $- \frac{1}{m}$ (the negative of its inverse).

Re-write the given equation $5 x - 2 y = - 1$ in slope-point form:
$y = \frac{5}{2} x + \frac{1}{2}$

The slope of the given equation is $\frac{5}{2}$
and the slope of a line perpendicular to it is $- \frac{2}{5}$

Apr 1, 2015

The slope is: $\left(- \frac{2}{5}\right)$

Perpendicular lines' slopes are negative reciprocals.

$y = \frac{5 x + 1}{2}$

The slope of line $y$ is: $\frac{5}{2}$

So $m \cdot \left(\frac{5}{2}\right) = - 1$

We need to find $m$ to find the slope of the perpendicular line.

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