5x + 4y = 7
4x - 5y = 5

I think the lines are neither. Just want to double check.

Thanks,
Cooper

First, put them in standard form (y=mx+b) where m is the slope and b is the y-intercept.

5x + 4y = 7
4y = -5x + 7
y = -5/4 x + 7/4

4x - 5y = 5
-5y = -4x + 5
y = 4/5 x - 1

The slopes will indicate whether they are parallel or perpendicular.

To be parallel, the slopes (-5/4 and 4/5) would have to be the same. They are not, so they are not parallel.

To be perpendicular, the slopes have to have opposite signs (they do) or be vertical and horizontal (they're not). The product of their slopes must equal -1:

-\frac 54 \,\times\, \frac 45 = -1

Oops. Looks like they're perpendicular.

I am glad I checked. I will go back and look at my work again and see what I did wrong. Thank you.