Question

why does slope have to be reduced to lowest term

Answer 1

There are infinitely many ways to write the same fraction. For example

1/2 = 2/4
1/2 = 3/6
1/2 = 4/8
1/2 = 5/10

I could keep going forever and I don't even need to use whole numbers. I could say

1/2 = 0.5/1
1/2 = 0.34/0.68
1/2 = 0.927/1.854

So because of this, it's handy to have some standard everyone can agree on. In this case, the common practice is to reduce fully. That way when it comes to grading papers, the teacher has an easier job and doesn't have to use a calculator for every possible fraction. In the work force, measurements are communicated much faster with this standard. Those are just two examples where the standard is handy.