Order in Linear Expressions

Date: 11/20/2001 at 11:01:57
From: Candi Mastroianni
Subject: Writing equations with proper order

Can you give me a convincing argument as to why, in an equation such 
as y = 13 - 7x, where y is a function of x, it should be written as
y = -7x + 13?

Date: 11/20/2001 at 12:54:24
From: Doctor Peterson
Subject: Re: Writing equations with proper order

Hi, Candi.

No, I can't. It can be written either way, depending on what is most 
important to you.

I would prefer 13 - 7x in many situations, just to avoid starting with 
a negative number and possibly dropping the sign.

I would prefer -7x + 13 in two situations: 

The first is when I am working with polynomials, which are 
traditionally written in decreasing order of degree, to make it easier 
to keep track of terms, particularly when multiplying or dividing, or 
even just comparing polynomials. 

The second is when I am showing an inexperienced student how this 
compares to the slope-intercept form, y = mx + b. For myself, I have 
no trouble seeing the slope as -7 regardless of the form, so I don't 
need to bother. And in fact, 13-7x makes the workings of the linear 
function clearer: you start at 13 on the y axis, and subtract 7 
whenever you increase x by 1. I could wish we wrote the formula as 
y = b + mx!

In short, the only reason to require a linear expression to be written 
as you suggest is to standardize students, as when a teacher wants to 
be able to grade tests quickly, or to develop habits that may be 
useful when they get to polynomials. Those aren't bad reasons; they 
just aren't absolute.

Now, are you the teacher, the student, or the parent? ;-)

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/