I don't understand. I looked at how to do it and used their same method, but I didn't arrive at the same answer as the one provided in the back of the book.

The question is:

Find equations of lines that pass through the point (3,8) and are (a) parallel to and (b) perpendicular to -4x+7y=-5.

The answer in the back of the book for this chapter test question is

OK, originally I messed up with the arithmetic, ugh. But I think I know how, am I right

You multiply the denominator and get 7y =4x-44 and move all the terms on one side...

4x-7y+44 = 0.