Order in Linear ExpressionsDate: 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/ |
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