Question

friends
why do write linear equation of two variable as
ax+by+c=0
why not ax + by - c = 0 or
ax + by = 0

Answer 1

ax + by = 0 always is a line passing through origin so this cannot be the answer because there are lines which don`t pass through origin

and regards +c it is mostly a convention/tradition that we don`t introduce - sign from our side so as to avoid any confusion

Answer 2

ax+by+c=0 passes through some points

Answer 3

ax+by+c = 0 can represent all lines

suppose it`s x+y+1 = 0 then this will not pass through all points in the x-y plane but only those which satisfy this condition

Answer 4

@msingh
clear?
if not can you elaborate your problem a bit

Answer 5

you know what dot product is @msingh ?

Answer 6

yes i know abt dot product,

Answer 7

but my question is y we write linear equation of two variable as ax+by+c=0

Answer 8

so in this case the equation ax+by=0 means all vector (x,y) perpendicular to (a,b).
and ax+by=c means all points whos position vector's projection on the normal to the line from the origin is constant and equal to c

Answer 9

ax+by=0 could be seen as a particular case of 2º point of few when c=0

Answer 10

it means when line passes trough the origin

Answer 11

this visión of the equation gives a very esay way to imagin it's position in 2D space. That's why it si used so much and even called a standart form