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 $\displaystyle 4x-7y+44 = 0.$

$\displaystyle y-8 = \frac{4}{7}(x-3)$

$\displaystyle 7(y-8)= 4(x-3)$

$\displaystyle 7y+56 = 4x-12$

$\displaystyle \frac{7y}{7}= \frac{4x}{7}-\frac{44}{7}$

$\displaystyle y = \frac{4}{7}x-\frac{44}{7}$

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.