Yahoo Answers: Answers and Comments for How can one straight line have two equations? [Mathematics]
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From Anonymous
enUS
Sun, 18 Nov 2018 19:43:34 +0000
3
Yahoo Answers: Answers and Comments for How can one straight line have two equations? [Mathematics]
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From az_lender: Sure, that's the same thing.
Multiply &quo...
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Sun, 18 Nov 2018 20:04:04 +0000
Sure, that's the same thing.
Multiply "your" equation by 3, you get
3y = 2x + 12, equivalent to
2x + 3y = 12.
The only thing "wrong" with yours is that you rounded off an inexact value, when the 0.666 probably should have been
0.66666666666666666 et cetera

From Samwise: There are an infinite set of equivalent equati...
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Sun, 18 Nov 2018 19:54:22 +0000
There are an infinite set of equivalent equations for any straight line.
The key here is that the equations have to be equivalent,
something we can check with a little algebra.
2x + 3y = 12
3y = 2x + 12 [subtracting 2x from each side]
y = (2/3)x + 4 [dividing each side by 3]
Taking your decimal fraction 0.666 as an approximation of 2/3,
the two equations are equivalent
[though, correctly rounded, it should have been 0.667,
and generally I'd prefer the exact fraction to the decimal approximation].
Were you told to give the answer in "standard form"?
Your answer [again, allowing for that decimal approximation]
is in slopeintercept form, not standard form.

From Raymond: The same equation can be written in different ...
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Sun, 18 Nov 2018 19:51:35 +0000
The same equation can be written in different ways.
Sometimes, for homework, you are asked (or expected) to write your answer in a specific way.
One format is called the "slope intercept"
y = mx + c
where m is the slope (how fast y increases when x goes up by 1)
and c is the intercept (the value of y, when x=0)
Yours appear to be
y = (2/3)x + 4
From there, you can go to any of the other "standard" formats.
Multiply both sides by 3
3y = 2x + 12
Add 2x to both sides
2x + 3y = 12
(this is, apparently, the format you were expected to use)
Subtract 12 from both sides
2x + 3y  12 = 0
(This is also known as a standard format).
If anything, you try to avoid fractions (if you can); also, if you are stuck with using a fraction, you try to make it a ratio of integers
(I suspect that your 0.666 was meant to represent 2/3, which is really 0.66666666666... forever)
In other words, 0.666 is not quite the same as 2/3.

From Some Body: So you got:
y = 2/3 x + 4
Multiply both side...
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Sun, 18 Nov 2018 19:51:20 +0000
So you got:
y = 2/3 x + 4
Multiply both sides by 3:
3y = 2x  12
Rearrange:
2x + 3y = 12
Both equations are the same, just written differently.

From derfram: Convert your answer into 'Standard' fo...
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Sun, 18 Nov 2018 19:50:51 +0000
Convert your answer into 'Standard' form
y = 0.666x + 4; multiply both sides of your equation by 3
3y = 2x + 12; add 2x to both sides
2x + 3y = 12; equation in 'standard' form

From Dixon: It is the same equation.
3y = 12 is considere...
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Tue, 20 Nov 2018 16:51:47 +0000
It is the same equation.
3y = 12 is considered to be the same equation as y = 4 or indeed 9y = 36 because they all tell you the same thing, ie that = 4.
Similarly, y = 0.666x is the same equation as 3y = 2x and 3y + 2x = 0

From Jeff Aaron: Those two lines are close but not exactly the ...
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Tue, 20 Nov 2018 15:42:02 +0000
Those two lines are close but not exactly the same.
If you multiply the first equation by 3, you get:
3y = 1.998x + 12
Add 1.998x to both sides:
1.998x + 3y = 12
If 0.666 was rounded off from 2/3, then in fact the two lines are the same.

From Amy: Taking a simpler line than your problem, consi...
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Tue, 20 Nov 2018 09:53:02 +0000
Taking a simpler line than your problem, consider the equation y = x.
This line goes through the points (1,1), (3,3), (2.7, 2.7), etc.
The "equation of a line" is a description of what paired values of x and y describe the set of points that are on the line. An equation is a statement that can be either true or false.
y = x is TRUE when x = 3 and y = 3.
It is false when x = 3 and y = 4.
Therefore the point (3,3) is on the line y=x, and the point (3,4) is NOT on the line y=x.
Now consider the line 2y = 2x.
You'll find that it describes the exact same set of points. This equation statement is true at all the same (x,y) values where y=x is true, and false at all the same values where y=x is false.
In general, multiplying both sides of an equation by the same number (except 0) will produce a different equation that has the same truth values.
y=x is the same as 2y=2x is the same as 17y=17x.
Adding the same number to both sides of an equation, or pretty much any mathematical manipulation done to both sides, produces an equation that describes the same line.
y = x1 is the same as y+1 = x is the same as y  3 = x  4.
This is an important principle for solving algebraic equations.

From Anonymous: 2x+3y=12.
3y=2x+12
y=(2/3)x+4
I assume you...
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Tue, 20 Nov 2018 09:00:00 +0000
2x+3y=12.
3y=2x+12
y=(2/3)x+4
I assume you meant to post this and not y=0.666x +4
2/3 is not the same as .666

From sepia: y = 0.666..x + 4
0.666..x + y = 4
2x + 3y = 12
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Mon, 19 Nov 2018 22:38:32 +0000
y = 0.666..x + 4
0.666..x + y = 4
2x + 3y = 12

From Philomel: Go to Kahnacademy.org and look at the equation...
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Mon, 19 Nov 2018 00:57:06 +0000
Go to Kahnacademy.org and look at the equation of a line.
y=mx+b id called the slope intercept form
ax+by= c is standard form.
Both of the equations you show are equal but in different forms.

From Jeffrey K: They are the same equation.
y = .666x + 4
mul...
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Sun, 18 Nov 2018 21:01:34 +0000
They are the same equation.
y = .666x + 4
multiply by 3
3y = 2x + 12
2x + 3y = 12

From alex: Not , It's not y=0.666x +4
It's y = ...
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Sun, 18 Nov 2018 20:48:09 +0000
Not , It's not y=0.666x +4
It's y = 2x/3 + 4
or
2x + 3y = 12

From Lotus: The straight line is the penis and the two equ...
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Tue, 20 Nov 2018 01:13:29 +0000
The straight line is the penis and the two equations are the balls

From arran: Get a life
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Tue, 20 Nov 2018 11:20:03 +0000
Get a life

From RealPro: 4 = 2 + 2 but also 4 = 1 + 3 so are you surpri...
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Sun, 18 Nov 2018 20:04:35 +0000
4 = 2 + 2 but also 4 = 1 + 3 so are you surprised about that as well? Cause that's basically the equivalent of what you're asking.
At this point, you should know how to REARRANGE EQUATIONS already.
Realize that a line is a set of points that have two coordinates (numbers) in order: x and y.
A point is a part of the line if its x and y satisfy the equation of the line when you put them inside it.
But then when you do the SAME THING to both sides of the equation, that does not change the equation. So the SAME pair of numbers x and y will STILL satisfy it.
y = (2/3)x + 4
Multiply by 3 on BOTH sides
3y = 2x + 12
Add 2x to BOTH sides
2x + 3y = 12
Two steps.
Also
x = 6  1.5y
2x + 3y  12 = 0
x/6 + y/4 = 1
2000x + 3000y = 12,000
So that's actually more than just 2.
Please try to understand you can't claim equality out of laziness.
2/3 = 0.666666666666666... forever. You can't stop at THREE sixes and say it's the same. At least say 0.666...