Equations of Lines and Normal Vectors

Equations of lines and normal vectors

We use numbers now, but you can substitute any letter for each variable. If you have ax
plus by plus c, the same story applies.
By the same reasoning, if the line ax + by + c = 0, then the vector (a, b) is perpendicular to
the line.
ax + by + c = 0
That's it.
Can zero be replaced with any number? Or, can it be like ax plus by plus c equals d? Yes,
that will still be true.

ax + by + c=d
It can be put differently. We can, for example, subtract off the c. So ax plus by equals d
minus c, which will appear a number. Or subtract off the d. Then it is like ax plus by plus c
minus d equals 0. It works that way.
One more tiny detail. The word normal means perpendicular. It is simply another word that
means exactly the same thing. Mathematicians often use the word normal when referring
to a vector that is perpendicular to a line.

Then, that red vector is the normal vector to the line.
[Graph]