Question

Prove that every straight line has an equation of the form Ax + By + C = 0, where A, B and C are constants.

Answer 1

Given a straight line

Either it cuts the y-axis, or is parallel to or coincident with it.

We know that the equation of a line which cuts the y-axis (i.e., it has y-intercept) can be put in the form y = mx + b; further

If the line is parallel to or coincident with the y-axis

Its equation is of the form x = x₁

Where x = 0 in the case of coincidence.

Both of these equations are of the form given in the problem and hence the proof.