Why is the standard form of a linear equation significant in graphing?

[DecayProduct]

Why is the standard form of a linear equation ax + by = c? What is the significance of this particular way of writing the equation that makes it "standard"? When we graph a line, we always transform the equation into something else, such as the point-slope form, y = mx + b.

In other words, what is the equation, without transformation, used for?

 

[snipez90]

Well I've always been told that it's for presentation purposes. But then again I view that equation as more of a diophantine equation anyways.

 

[kenewbie]

I'm guessing a sorted polynomial form makes it easier to read and factor the thing? It doesn't really matter for a linear equation, but once you get higher degrees it does make a difference.

A quick glance at the first factor tells you the degree, you can easily locate the constant, you can quickly see if it is a complete square. If it was written as a slope, some of those would take longer.

k

 

[HallsofIvy]

One advantage of that form is that every line can be written in that form. A vertical line, say one in which x is always 3, has the form x= 3, of course, which is ax+ by= c with a= 1, b=0, c= 3. It cannot be written in the form y= mx+ b because solving ax+ by= c for y involves dividing by b which, here, is 0. Additionally, in y= mx+ b y is necessairily a function of x. If x= 3, that is not true.