In the equation, we need at least one variable not equal to zero.
Suppose in the same example that you have mentioned, if a and b, both are equal to zero,
then the equation becomes, a x 0 +b x 0 + c =0
That is, the equation reduces to c = 0.
And if the constant is also zero, there is no point in defining the equation.
Take the example of 4 - 3x = 0
Here the coefficient b = 0 and hence 3x = 4, that is x = (4/3)
So in the number line it represents a point (4/3) and in the cartesian plane it represents a
line parallel to y-axis, and its equation is x = (4/3)
Suppose the equation is 4 - 3y = 0.
Here, a = 0 and b = -3
Therefore, we have y = (4/3)
Again in the number line it represents a point (4/3) and in the cartesian plane it represents a
line parallel to x-axis, and its equation is y = (4/3)
So for a linear equation either of the coefficients shoud be a non-zero real number.