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.
It is exactly if you multiply the equation by -1.
Yes, that is how they got those equations.Although when I do this:
I get something that resembles the equation in the second part:
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.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.
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.)