there are some values of a,b&c for which the equation ax+by+c = 0 does not represent a straight line.give ex.?

Question

give an example of such values please.

Answer 1

If
a = x
b = y

then you get
x^2 + y^2 + c = 0

which is a circle, not a straight line.

Answer 2

The only way this does not represent a straight line is if a=0=b, because then it says c = 0 which is tautological if c = 0 and false otherwise.

If a = 0 = c, the equation is by = 0, which is the x axis (a straight line, surely!) provided b ≠ 0. If a = 0 but c ≠ 0, we have by = c which is a straight line parallel to the x axis.

It's always a straight line, except in the weird cases I described above. But, after posting this, I see the first answer covered it in different words. Take no notice of the answers between the first one and this, they're barking up the wrong tree.

Answer 3

If a, b, and, c are real numbers, then ax + by = c is the equation of a line except when a = 0, b = 0, and c = 0. In that case, ax + by = c is 0x + 0y = 0 or 0 = 0.

You may also want to consider complex numbers of the form a + bi where a and b are real numbers and i is the imaginary unit.

For example, is (2 + 3i)x + (5 - i)y = 3 + 4i a line?

Answer 4

If the equation is defined at all, it'll be a straight line. You can rearrange it to y = -(a/b)x - c/b

You only get weird results is if b = 0. Then you can't solve for y, since doing so would involve dividing by zero. The original equation turns into ax + c = 0, which turns into x = -c/a. The equation would still give you a straight line (as long as a isn't zero), but it would be a vertical line.

The only time you don't get a straight line at all is if a and b both equal zero. Then the equation turns into c=0, which is either a true statement or a false statement (depending on what value you had assigned to c), but is not the equation of a line.

Answer 5

If a, b, and c are real numbers, ax + by + c = 0 always is a line EXCEPT in cases where a=b=0. In that case c=0, which is not geometric, and is a falsehood unless c is actually zero. (That is if a=b=0 and c=2, you cannot have 2=0.)

If a=0, you have a horizontal line with y-intercept -c/b.

If b=0, you have a vertical line with x-intercept -c/a.

If c=0, you have a line with slope -a/b, passing through the origin (y-intercept 0).

If a=c=0 or b=c=0, you have special cases I cited for a=0 or b=0 where the intercept is 0.

If a=b=c=0, you have the statement 0 = 0. Solutions would be the entire (x,y) plane.

Answer 6

If a, b and c are all constants, ax+by+c=0 will always give you a straight line. If a,b or c is a function, or an imaginary number, the situation may be different...

Answer 7

Assuming you're dealing with 2d space...
If a=b=0, then:
If c=0, the entire xy plane satisfies the equation.
If c<>0, there is no solution.

In 3d (or higher) space, there is no linear solution.