Perpendicular lines have slopes that are opposite signs and reciprocals.
For example, the perpendicular slope to 2/3 is -3/2 (opposite sign and flipped upside-down).
The first step on your question is to find the slope of your line. You can do this by putting the equation into slope-intercept form:
[tex]\begin{aligned}4x-5y &= 10\\[0.5em]-5y &= -4x+10\\[0.5em]y &= \dfrac{4}{5}x-2\endaligned}[/tex]
From this, we can see your slope is 4/5.
The perpendicular slope will be -5/4.
