Answer
Perpendicular
Work Step by Step
To determine if the lines are parallel or perpendicular, we compare their slopes.
We start with the line $5x-8y=3$:
$5x-8y=3$
$8y=5x-3$
$y=\frac{5}{8}x-\frac{3}{8}$
So this line has a slope of $\frac{5}{8}$.
Next, we look at the line $10y+16x=1$:
$10y+16x=1$:
$10y=-16x+1 $
$y=-\frac{8}{5}x+\frac{1}{10}$
This line has a slope of $-\frac{8}{5}=-\frac{1}{5/8}$
Since the two slopes are negative reciprocals of each other, the lines are perpendicular.
