# Thread: Equation of a line??

1. ## Equation of a line??

Ok, I am after your views on this?

Is (y-2)/x = 3 the equation of a line?

Do we need to worry that it is not defined for x=0 ?
Obviously, it can be re-arranged into a standard form, but in this form what do we conclude?

2. ## Re: Equation of a line??

Originally Posted by rodders
Ok, I am after your views on this?

Is (y-2)/x = 3 the equation of a line?

Do we need to worry that it is not defined for x=0 ?
Obviously, it can be re-arranged into a standard form, but in this form what do we conclude?
Well of course we must always be concerned if the expression is not defined somewhere.
Look at this plot.
There is an unexpected 'whole' in the plot. The graph is not continuous.
Then is that a line? Or even a linear relation? What do YOU say?

3. ## Re: Equation of a line??

Originally Posted by Plato
Well of course we must always be concerned if the expression is not defined somewhere.
Look at this plot.
There is an unexpected 'whole' in the plot. The graph is not continuous.
Then is that a line? Or even a linear relation? What do YOU say?
I plotted it in desmos and it didn't distinguish between y= 3x+2 and the form above!
I say its a line everywhere except x=0 !

4. ## Re: Equation of a line??

Originally Posted by rodders
I plotted it in desmos and it didn't distinguish between y= 3x+2 and the form above!
I say its a line everywhere except x=0 !
In that case you must tell us what definition allows for a line to have a dis-continuity.

I do not know of one. Whether in geometry or analysis lines are continuous. They have the property that a point is between two points on a line then that point is also on the line. In the case you present, I would say that we have the union of two half-lines: $(-\infty,2)\cup(2,\infty)$

I see....

6. ## Re: Equation of a line??

Originally Posted by Plato
In the case you present, I would say that we have the union of two half-lines: $(-\infty,2)\cup(2,\infty)$ $\ \ \ \ \ \ \$ apparent typo
$(-\infty,0)\cup(0,\infty)$

7. ## Re: Equation of a line??

Originally Posted by greg1313
$(-\infty,0)\cup(0,\infty)$
I actually did mean $(-\infty,2)\cup(2,\infty)$. But should have said that is a description of the image space.