#### red and white kop!

##### Junior Member

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cant find any

- Thread starter red and white kop!
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cant find any

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What happens, if all of the parameters are zero?

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is this the only case? a, b and c being all equal to zero?

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red and white kop! said:is this the only case? Nope, but the cases requested all involve zero(s) somewhere.

Consider all the possibilities that involve zero; there aren't that many cases to consider.

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if a and b are 0 then the result is c=0

if a is 0 then the result is by=-c, which is a horizontal line

if b is 0 then the result is a vertical line

and then of course there is if a and c are 0 and if b and c are 0 but the truth is i just dont know what to conclude from these results

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hey i'd really need some helpfum insight on this one

If they are not constants, it won't be a line.

A linear equation requires a, b, and c to be constants.

(Well, c could be a multiple of x in theory).

If a, b, or c are functions of x, the function will bend in some way.

\(\displaystyle y=mx+c\\) is a line, even if m is zero, or if c is zero.

It's the x-axis if both m and c are zero.

If we rearrange that, we get \(\displaystyle mx-y+c=0\)

which is written as ax+by+c=0.

If b and c are zero, that's the y-axis.

a, b and c equal to zero means nothing at all.

So, linear equations have the powers of x and y equal to 1 in that form.

"Linear" means "straight line", a curved line is a curve.

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You've been given the General Form of a line.

(With beginning algebra, I think it's clear enough for tutors that the parameters are all constants.)

Let's read the formal definition:

Ax + By + C = 0, where A, B, and C are all Real numbers AND where A and B are not both zero.

There's your answer. Do you "see" it?

·

red and white kop! said:if all parameters are 0 then the result is 0=0 This equation contains no variables, so it cannot define a line.

if a and b are 0 then the result is c=0 Since c is non-zero, this equation is never true, so there is no line.

if a is 0 then the result is by=-c, which is a horizontal line Correct.

if b is 0 then the result is a vertical line Correct.

and then of course there is if a and c are 0 and if b and c are 0 but the truth is i just dont know what to conclude from these results

Then try some Real numbers for these last two cases, and see what happens. It takes only a few moments, to experiment.

a = 0

b = 1

c = 0

a = 1

b = 0

c = 0

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So, you can supply as many examples as needed; make A and B zero, and make C any number.