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#1 2006-12-19 03:12:23

Toast
Real Member
Registered: 2006-10-08
Posts: 1,321

unimportant (idiotic) line question

I was just fiddling while drawing linear relations graphs and I tried substituting a line with equation x=0 into y=mx+c.
The y coordinate picked is 0, so we have:
0=...
At this point x also = 0, so we have:
0=...0...
Add the constant:
0=...0+c
And the gradient:
0=∞×0+c
c=-∞×0=undefined
Thus the equation x=0, infact, really is y=∞x-∞(0), which is undefined. Am I right or am i right? wave

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#2 2006-12-19 04:08:21

gnitsuk
Member
Registered: 2006-02-09
Posts: 121

Re: unimportant (idiotic) line question

All straight lines in 2 dimensions can have their equations written in the form:

Call this equation (1)

It doesn't matter if the line is horizontal,vertical or anything inbetween.

We could rearrange equation (1) into this form:

Call this equation (2)

This is now in the form y = mx + c

where m = -a/b and c = -d/b

But this function will not be defined if b = 0. Take the example of the line x = 0. Now the points (0,K) and (0,L) are on this line and equation (1) gives us:

and

giving:

and

But this is only possible if b and d both equal zero - crucially b = 0. Thus equation (2) will be undefined. You cannot use the "y = mx + c" version of the formula to describe vertical lines as a vertical line implies b = 0 in equation (2) and equation (2) is not defined when b = 0. But equation (1) IS defined and for the line x = 0 you just set a = 1 and b = d = 0.

As a final example take the line y = x, this is in the "y = mx + c" form and that's okay as b is not equal to zero. The equation (1) form of this line is:

and so a = 1, b = -1 and c = 0 (Crucially b is NOT equal to zero and so the "y = mx + c" form is defined and so we can use it: y = x).

As a lead to other topics note that:

is the equation of a plane in 3 dimensions.

Last edited by gnitsuk (2006-12-19 04:10:57)

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