#### Answer

$$-\frac{1}{4}$$

#### Work Step by Step

The equation of the line given by
$$8x=2y-5$$
can be rewritten as
$$2y=8x+5$$
or
$$y=4x+\frac{5}{2}$$
The equation of a line in slope-intercept form is
$$y=mx+b$$
where $m$ is the slope and $b$ is the y-intercept.
For this line the slope is
$$m=4$$
For a line perpendicular to the original, the slope is the negative reciprocal
$$m=-\frac{1}{4}$$