Linear Equations - Standard Form

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Weevil

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Sep 24, 2008
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I have to change some equations to linear form and I really have no idea what I'm doing. I know you have to do something with AX+BY=C, and that's pretty much it. If I could just get someone to give a me few examples with the steps of the first three problems I think I could figure out the rest myself.

1. y=7x-5
2. x=-2/7y+3/4
3. 3y-5=0

I think #1 is 7x-y=5 and #2 might be 28x-8y=21, but like I said before I really don't know. I stayed up too late last night and fell asleep in algebra class. :oops: Not a very good idea...
 
Weevil said:
I have to change some [linear] equations to [standard] form and I really have no idea what I'm doing ... AX + BY = C ...

1. y=7x-5
2. x=-2/7y+3/4
3. 3y-5=0

I think #1 is 7x-y=5 and #2 might be 28x-8y=21, but like I said before I really don't know ...
Click to expand...

Hello there:

I do not agree with SparkNotes. The general form and standard form are distinct.

(Ax + By + C = 0 is the general form for a line when A and B are not both zero.)

Ax + By = C is the standard form for a line, where A, B, and C are integers whose greatest common factor is 1, A and B are not both equal to zero, and A is non-negative (when A = 0, then B has to be positive). The standard form can be converted to the general form by moving the constant to the lefthand side.

Note that C does not represent the same number in both forms unless it is zero.

7x - y = 5 is standard form.

A = 7
B = -1
C = 5

(The general form of this equation is 7x - y - 5 = 0.)

28x - 8y = 21 is also standard form.

A = 28
B = -8
C = 21

(The general form is 28x - 8y - 21 = 0.)

There are a few other forms for linear equations besides the standard, general, and y-intercept forms shown here (eg: point-slope form, normal form, intercept form, parametric form).

Intercept form is rarely seen, but it's interesting.

x/A + y/B = 1

where A is the x-intercept and B is the y-intercept. Obviously, neither A nor B can be zero, so this form only applies to lines that cross both axes at different locations (i.e., not at the origin).

You can switch from standard form to this form by dividing both sides by C.

For the first equation you posted (7x - y = 5), this division yields

x/(5/7) + y/(-5) = 1

The x-intercept is A = 5/7, and the y-intercept is B = -5.

Cheers,

~ Mark :)
 
Shouldn't tell him that masters: now he's gonna ask for a raise :lol:
 
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