Thread: Confused about equation of a line

Equation says this:


But the book tells me it can also be written like this:


I got confused on how that could be so I tried to get the second expression of a line from the first expression of the line by trying cross multyplication:


But I get this which is close but not it:


Although when I do this:


I get something that resembles the equation in the second part:


Am I doing something wrong here? How does this form a line exactly because I grew up with the y = mx+b equation and this is the first time I am seeing this.

Originally Posted by Bman900

Equation says this:

But the book tells me it can also be written like this:

What the text calls is actually two planes.
The given line is the intersection of those two planes.

Originally Posted by Bman900

Equation says this:


But the book tells me it can also be written like this:


I got confused on how that could be so I tried to get the second expression of a line from the first expression of the line by trying cross multyplication:


But I get this which is close but not it:

It is exactly if you multiply the equation by -1.

Although when I do this:


I get something that resembles the equation in the second part:

Yes, that is how they got those equations.

Am I doing something wrong here? How does this form a line exactly because I grew up with the y = mx+b equation and this is the first time I am seeing this.

y= mx+ b is the equation of a line in the plane. In three dimensions, you need 2 equations to specify a 3- 2= 1 dimensional line. A single equation in three variables determines a 3- 1= 2 dimensional surface.

You can break

into two independent equations just as you did. (There are other ways to form new equations but they are not independent equations.)

Ah I see it now, I was thinking about multiplying it by -1 but I was wondering why didn't they just leave it the way it comes out of cross multiplication. Anyway thank you for the help!