This is easy!  Look at these parallel lines:
a graph of two parallel lines

What do they have in common?

The same slope!

So, two lines are parallel if they have the same slope.

The problems in this section (and the next) are cool because they pull together a bunch of stuff I've shown you.

Check it out:

Let's find the equation of the line that passes through the point

( -3 , 5 ) and is parallel to the line   2y - 4x = 1  .

* To get the equation of a line we need:

1 a point -- which we have
a slope -- which we can get from   2y - 4x = 1

(since they are parallel, they'll have the same slope.)