Thread: line

considering an equation ax + by + c =0, im supposed to give examples of a, b, c for which the equation does not represent a straight line
cant find any

a=0
or
b=0
(c any rational number <>0)
by this you will only get a point but no line
if a=b=c=0
even this will not represent a st. line

if a=0 then the equation becomes by+c=0
by=-c
this is a horizontal line, but a line nevertheless, am i right?

yes ur right !
my bad
(y=k is a st line parallel to x axis)
but a=0,b=0,c=0
will not be a st.line for sure
see
0x+0y+0=0
this will be satisfied by all the points in the plane

any other situations which would fit the condition? such as other combinations of the parameters equalling zero?

ax+by+c=0
then
a=-(by+c)/x
now if y,c,b,x are rational numbers then a will also be a rational number (case of 0 has already been discussed)
so i don't think there is any value of a,b,c (except a=b=c=0) for which equation ax+by+c=0 do not represents a line.