Determine if the lines are parallel, perpendicular, or neither 4x+5y=10 and 5x - 4y =28

Turning both equations into y=mx+b would be the first step. With the first problem you would subtract 4x from both sides and being left with 5y=-4x+10 and then you divide both sides of the equation by 5 to get the y alone so that leaves you with y=-4/5x+2
For the second problem you subtract 5x from both sides and are left with -4y=-5x+28 and then you divide both sides of the equation by -4 to get y alone and that leaves you with y=5/4x-7
So looking at the slopes -4/5 and 5/4 which they are reciprocals of each other so these lines are perpendicular.