What is "standard form" of linear equations? Or is there such?

[lookagain]

From this thread:

y- (3/2)x= -6- 15/2

y- (3/2)x= -27/2 which is of the form Ax+ By= C \(\displaystyle \ \ \ \ \)No, it is not of that form. Please see below.

with A= -3/2, B= 1, and C= -27/2.

If you don't like fractions (or negative numbers) then multiply on both sides by -2,

as Soroban suggests: 3x - 2y = 27 \(\displaystyle \ \ \ \ \ \) <-------- Not only is this in Ax + By = C form, but certain
instructors would mark the answer as "incorrect" if it were written in any other form.

Standard Form of lines:

1) All coefficients in Standard Form are integers if possible.

2) The x-term is to the left of the y-term.

3) It is common for the coefficient of the x-term to be positive.

4) It is common for the coefficients of the x and y-terms to be
\(\displaystyle \ \ \ \ \ \)relatively prime to each other.

 

[Ishuda]

Standard Form of lines:


1) All coefficients in Standard Form are integers if possible.

2) The x-term is to the left of the y-term.

3) It is common for the coefficient of the x-term to be positive.

4) It is common for the coefficients of the x and y-terms to be
\(\displaystyle \ \ \ \ \ \)relatively prime to each other.

Shows what time will change. When I was going to school, some mumble mumble years ago, the standard form was
y = A x + B
This 'new' standard form certainly allows for all lines, even the limiting form where B = -A C and allowing A to approach infinity.

BTW: You can always satisfy (2) and (3) but which do you satisfy when you can't satisfy both (1) and (4).

 

[HallsofIvy]

Standard Form of lines:


1) All coefficients in Standard Form are integers if possible.

2) The x-term is to the left of the y-term.

3) It is common for the coefficient of the x-term to be positive.

4) It is common for the coefficients of the x and y-terms to be
\(\displaystyle \ \ \ \ \ \)relatively prime to each other.

Can you give a reference for this? In any case, the original post said nothing about "standard form". It said only "Write the equation in the form Ax + By = C".

 

[lookagain]

Can you give a reference for this? \(\displaystyle \ \ \ \ \ \)Yes, I give several below.

In any case, the original post said nothing about "standard form". \(\displaystyle \ \ \ \ \ \) The equation spelled out what it means for
the look of the Standard Form of a line.

It said only "Write the equation in the form Ax + By = C". \(\displaystyle \ \ \ \ \ \)In the context of writing equations of lines,
that necessarily means to write the equation in Standard Form.

y- (3/2)x= -27/2 which is of the form Ax+ By= C ...

Anyway, your terms on the left-hand side of the equation are in the wrong order.

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References:


Standard Form of a Line

Standard Form of a LineDay 6: Standard Form of a Line by: BJ Jackson Ojectives: 1. to be able to write the equation of a line in standard form. Definitions:
View on jwilson.coe.uga.edu	Preview by Yahoo​

Mathwords: Standard Form for the Equation of a Line

Mathwords: Standard Form for the Equation of a Line---
View on www.mathwords.com	Preview by Yahoo​

Math Forum - Ask Dr. Math

Math Forum - Ask Dr. MathWhat is standard form? What does Ax+by = c mean and what do the letters stand for?
View on mathforum.org	Preview by Yahoo​

Point Slope Form and Standard Form of Linear Equations

	​
Point Slope Form and Standard Form of Linear EquationsPoint Slope Form and Standard Form of Linear Equations Learning Objective(s) Give the point slope and standard forms of linear equations and define their...
View on www.montereyinstitut...	Preview by Yahoo​

Standard Form for Linear Equations

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Standard Form for Linear EquationsStandard Form For Linear Equations This page assume that the reader understands the following concepts: The coordinate plane. Graphing lines on the coordinate plane.
View on courses.wccnet.edu	Preview by Yahoo​

http://www.mathsisfun.com/algebra/standard-form.html

/\/\ Scroll down until you see the appropriate subsection.



http://hotmath.com/hotmath_help/topics/standard-form.html



http://www.ck12.org/book/Algebra-I/r2/section/5.3/